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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf,len=1435
+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  ©ESO 2023  January 5, 2023  Identifying preflare spectral features using explainable artificial  intelligence  Brandon Panos1, 2, Lucia Kleint1, 2, and Jonas Zbinden1, 2  1 University of Geneva, 7, route de Drize, 1227 Carouge, Switzerland  2 Astronomical Institute of the University of Bern, Sidlerstrasse 5, 3012 Bern  Received 29 August;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Accepted 24 December 2022  ABSTRACT  The prediction of solar flares is of practical and scientific interest;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' however, many machine learning methods used for this prediction  task do not provide the physical explanations behind a model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We made use of two recently developed explainable  artificial intelligence techniques called gradient-weighted class activation mapping (Grad-CAM) and expected gradients (EG) to  reveal the decision-making process behind a high-performance neural network that has been trained to distinguish between Mg ii  spectra derived from flaring and nonflaring active regions, a fact that can be applied to the task of short timescale flare forecasting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The two techniques generate visual explanations (heatmaps) that can be projected back onto the spectra, allowing for the identification  of features that are strongly associated with precursory flare activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We automated the search for explainable interpretations on the  level of individual wavelengths, and provide multiple examples of flare prediction using IRIS spectral data, finding that prediction  scores in general increase before flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Large IRIS rasters that cover a significant portion of the active region and coincide with  small preflare brightenings both in IRIS and SDO/AIA images tend to lead to better forecasts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The models reveal that Mg ii triplet  emission, flows, as well as broad and highly asymmetric spectra are all important for the task of flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, we  find that intensity is only weakly correlated to a spectrum’s prediction score, meaning that low intensity spectra can still be of great  importance for the flare prediction task, and that 78% of the time, the position of the model’s maximum attention along the slit during  the preflare phase is predictive of the location of the flare’s maximum UV emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Sun: flares;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' chromosphere — line: profiles — methods: data analysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' statistical  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Introduction  A solar flare is a sudden release of energy due to magnetic  reconnection, resulting in an enhancement across the entire  electromagnetic spectrum (Carmichael 1964;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Sturrock 1966;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Hirayama 1974;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Kopp & Pneuman 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Low 1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For large  flares this energy can reach an order of ∼ 1032 ergs (Aulanier  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2013), and is used to accelerate charged particles toward  and away from the solar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The energy dissipates over  stages with timescales that vary from seconds to hours (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=',  Fletcher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The outward bound material fills the  interplanetary medium with high-energy particles and perturbs  the heliospheric magnetic field (Rouillard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2016), both  of which interact with Earth’s magnetosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These events,  if directed toward Earth, can trigger power grid blackouts and  adversely affect communication systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Boteler 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Schrijver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2014), which in today’s technologically saturated  environment comes with a high socioeconomic cost, making  their prediction critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Machine learning has provided us with a set of powerful al-  gorithms that can be used to attempt to predict whether an active  region (a patch on the Sun associated with enhanced magnetic  activity), will produce a flare or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' One of the most successful  algorithms for such a task is the so-called neural network (NN)  (Rosenblatt 1958), which is a computational graph-like structure  that draws inspiration directly from the mammalian brain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Just as  an organic brain, these networks automatically program them-  selves through experience (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2016) and can  generalize what they have learned to make informed decisions  about new observations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Vidyasagar 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The majority of flare prediction efforts rely on full photo-  spheric vector magnetograms recorded by the Helioseismic and  Magnetic Imager (HMI, Scherrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Hoeksema et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  2014) onboard the Solar Dynamic Observatory (SDO, Lemen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These photospheric magnetic data are typically fed  into a machine learning algorithm such as a NN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Bobra &  Couvidat 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Florios et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Soós et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In terms of the true skill statistic (TSS), the standard met-  ric for evaluating a model’s predictive performance (1 being op-  timal and -1 being adverse), the expected baseline TSS using  data from SDO is around ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='7, regardless of the sophistica-  tion of the machine learning algorithm (Jonas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This  indicates an apparent bottleneck and limit to the utility of photo-  spheric magnetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  As a way to overcome this bottleneck, researchers have  started experimenting with novel parameterizations of the HMI  magnetic data using topological data analysis to codify their rich  spatial features (Deshmukh, Varad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Deshmukh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Moreover, additional information from complementary  data sources such as soft X-ray, flare history, and AIA photo-  spheric, chromospheric, and coronal images have been incorpo-  rated in an attempt to improve model performance (Nishizuka  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Jonas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  New evidence suggests that high resolution spectral data  can be used to predict solar flares at least on short subhour  timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Panos & Kleint (2020) created two classes of Mg ii  spectra captured by NASA’s Interface Region Imaging Spectro-  Article number, page 1 of 21  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='01560v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='SR]  4 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  graph (IRIS) (De Pontieu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The first class consisted of  spectra from active regions that did not lead to solar flares (here-  after referred to as the AR class), and the second one consisted  of spectra collected from active regions 25 minutes before flare  onset (referred to as the preflare PF class).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It was demonstrated  that a simple feed forward fully connected NN could distinguish  between spectra from either class with an 80% accuracy, pre-  cision, and recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Furthermore, the network’s performance in-  creased monotonically when successively feeding spectra from  t = 30 to t = 0 minutes before the onset of a large X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6-class  flare, albeit over a restricted region of the slit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is not, however,  clear why the network performed so well at the classification  task, and on what grounds it based its decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Nevertheless,  these results open up the possibility of not only improving the  current performance of our models, but due to the high diag-  nostic capabilities of spectra (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Leenaarts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2013), could  also provide critical information about the state of the preflare  atmosphere, and any necessary conditions that might facilitate a  solar flare (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Yang 2019), thus shifting the focus from model  performance to physical understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Along these lines, and in an attempt to explain the above  results, a recent study made use of a clustering technique to  identify common spectroscopic precursors and atmospheric  conditions that might facilitate flare triggering events (Woods  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It was found that single-peak emission in both the  Mg ii h&k lines as well as the pair of subordinate lines located  at ∼ 2798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8 Å appeared most commonly, but not exclusively,  within the study’s PF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Inversions of these single-peaked  profiles using the STiC inversion code (de la Cruz Rodríguez  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019) indicate enhanced chromospheric temperatures and  electron densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Similar to previous findings (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Cheng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1984;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Machado et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Harra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Panos &  Kleint 2020), the authors speculate this to be a consequence of  small-scale heating events possibly driven by reconnection as  far back as 40 minutes before flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since this clustering  approach of identifying important PF spectra is manually inten-  sive and time-consuming, a recent study automated the process  via the use of multiple instance learning (MIL) (Huwyler &  Melchior 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In addition to high accuracies on the AR/PF  classification task, their models automatically identified spectra  that were judged to be important for flare prediction, confirming  the results found in Woods et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Their work however  does not indicate the particular features of each spectrum that  are responsible for high model scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  For this study, we made use of the same Mg ii dataset from  the original paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We then trained a powerful "visual" NN called  a convolutional neural network or ConvNet on the AR/PF binary  classification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Once the model learned to distinguish be-  tween AR and PF spectra, we used a class of techniques, col-  lectively referred to as Explainable Artificial Intelligence (XAI)  (Barredo Arrieta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019) to derive direct explanations from  the ConvNet without having to perform intermediate manual  steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These techniques allowed us not only to automatically  discover which spectra are important, but which features of the  spectra are most critical for predicting solar flares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Data  The data used in this study are composed of Mg ii spectra cap-  tured by the IRIS satellite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For consistency, the dataset is iden-  tical to that used in Panos & Kleint (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' As before, we se-  lected a spectral window spanning 2794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='14 − 2805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='72 Å, which  includes both the Mg ii h&k lines as well as the triplet emission  around 2798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='77 Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We then partitioned observations into two  classes based on the GOES soft X-ray flux: The first partition  is called the AR class, and is composed of roughly 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='5 million  spectra derived from 18 observations and extracted from a 25  minute window at the start of each observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An observation  here means a period with a predefined observing scheme, which  can last several hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The only criterion for an observation in  this class was that a large flare (M- or X-class) did not appear  over the entire duration of the IRIS observation, as verified by  the GOES X-ray flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This does not preclude smaller flares such  as C-class and lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since this study probes short timescales  (as apposed to the normal 24 hour margins used in flare predic-  tion studies), it is not guaranteed that the active region did not  produce a large flare after the IRIS observation’s time window  ended, leading to a possible weak mixing of the classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The second partition is called the PF class and consists of  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4 million spectra taken from 19 observations in a time window  25 minutes (sometimes shorter if IRIS was not recording) before  each X- or M-class flare’s onset as defined by the NOAA catalog  flare start time (Table 1 of the same study).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Like previous studies  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Jonas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Angryk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2020), we do not consider  small flares (<M-class) as targets for prediction, but rather as  a set of important features whose frequency could help predict  larger events, meaning that smaller flares were not necessarily  precluded from the 25 minute analysis window for both the AR-  and PF class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  An example of a PF (top) and AR (bottom) observation can  be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The gray regions indicate the 25 minute time  windows over which Mg ii spectra were collected with the time  in minutes on the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' As indicated by the GOES 1 − 8 Å  flux (solid blue curve) and flare class along the y-axis, a large  M-class flare occurs in the PF observation directly after the sam-  pling region, while the AR observation is flat and then slightly  raises to a C-class level towards the end of the observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is  important to remember that GOES integrates the X-ray flux from  the entire solar disk while IRIS observes only a small patch of  the sun (a maximum of 175 × 175 arcsec2 for the slit-jaw imager  and 130 × 175 arcsec2 for its spectrometer), therefore, although  the large flares were visually confirmed to be within IRIS’s field  of view (and indeed at some future point crossing the spectro-  gram), the X-ray signals in the AR class could have occurred  somewhere else on the solar disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each interval between the ver-  tical black dotted lines indicates the completion of a single IRIS  raster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If the observation is a sit-and-stare, meaning no spatial  rastering of the spectrogram, as in the AR example, then the  intervals indicate the individual exposure times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For context, a  SJI accompanies each figure and was rendered roughly around  the time indicated by the vertical blue dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The blue re-  gions within each SJI indicate the spatial extent of the IRIS raster  which is spanned by steps of equal size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each flare was assigned  a number in the title for future reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  After sampling the spectra using the above prescriptions, a  series of additional processing steps were performed on the al-  ready preprocessed IRIS level 2 data to make it amenable to  machine learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These steps were as follows: 1) All  spectra were interpolated to a grid size of 240 λ-points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2) Each  spectral profile was normalized by its maximum value, effec-  tively placing precedence on the shape of the Mg ii spectra in-  stead of their intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is important to keep in mind that the  intensity is still weakly encoded into the spectral shape, since  high intensity profiles, once normalized, will result in spectra  with flat continuum emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To avoid noisy and corrupt data,  entire spectra were replaced with nan’s if they met any of the fol-  lowing conditions: Missing data → If a spectrum (within our se-  Article number, page 2 of 21  Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Example of data collection for a single PF (top) and AR (bottom) observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Mg ii spectra in both cases were extracted from the gray  time interval with the interval between each vertical dashed line indicating the completion of a single raster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For context a SJI is included for each  observation at the time roughly indicated by the vertical dashed blue line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The blue curves in the time plots indicate the integrated GOES flux in  the 1−8 Å channel, while the blue regions in the SJI indicate the span of the raster, with a four step raster for the PF observation and a sit-and-stare  for the AR observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  lected wavelength window) contained at least one value < −100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Overexposure → If 10 consecutive intensity values were equal  to the maximum intensity value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is quite a high threshold  and in retrospect should be decreased, however, for the sake of  continuity with previous results we maintain this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Poor  signal-to-noise → Any spectra that remained below a 10 DN/s  threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Cosmic rays → If the maximum intensity value ap-  peared outside of a small window surrounding both the h&k-  cores, or if the k/h-ratio exceeded the theoretical limits of 2:1 or  1:1 by a value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3, that is spectra with ratios exceeding 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3 or  less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='7 were excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, the reconstruction er-  ror of a variational autoencoder trained on quiet Sun spectra was  used as a way to dynamically mask spectra that are typically as-  sociated with quiescent Sun observations, see Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' (2021)  for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Model development  In this section, we build up the intuition necessary to understand  how our machine learning algorithm predicts whether a spectrum  comes from a nonflaring or flaring active region by introducing a  general set of machine learning principles and training etiquette.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We then discuss our particular case, including a description of  the model that we use (a ConvNet), and how IRIS data in combi-  nation with the search for quality explanations in addition to high  performance, forces us to modify the standard training practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Problem outline  Our goal is to create a function/model FΘ(x) → ˆy, that is pa-  rameterized by a set of arguments {θ | θ ∈ Θ}, and can take as  input a raw spectrum x ∈ X from the dataset, and produce an  output probability ˆy ∈ [0, 1] representing the model’s guess as  to whether the spectrum belongs to either the AR (output closer  to zero) or PF class (output closer to one).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The objective is to  find a set of parameters {θ}, referred to as the model’s weights,  that generates the closest match between the actual set of labels  {yn} and the predicted set of labels {ˆyn}, for example, we want a  model that can correctly predict the class of as many spectra as  possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This type of problem is referred to as a binary classifi-  cation problem and can be solved using any number of methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The optimal parameterization is usually found by introducing a  loss function L(y, ˆy, Θ), that when minimized, guides the model  parameters in a controlled manner to their optimal values {θ∗}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  This process of incrementally adjusting the model’s weights is  referred to as training and is achieved via gradient descent, that  is, by taking the derivative of the loss function ∂θL(θ) with re-  spect to the weights, and adjusting those parameters in small in-  crements in the direction that results in the largest decrease to  the loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since the objective is simply to have a model make as  many correct label predictions as possible, the loss function de-  pends on the true and predicted labels as well as its internal set  of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To train our models we made use of the binary  cross-entropy (BCE) loss function (with regularization)  L(y, ˆy, Θ) = − 1  N  N  �  n=1  �  yn log FΘ(xn)  + (1 − yn) log [1 − FΘ(xn)]  �  + λ  M  �  m=1  θ2  m,  (1)  which is a measure of dissimilarity between the true set of labels  {yn} and the predicted set of labels {ˆyn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If the differences be-  tween these two sets is large, then the loss is also large, and vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In terms of information theory, the BCE is the average  Article number, page 3 of 21  Flare#13OBSID:3860258971  10-3  Steps:4  SJI1330  (-216",204")  extracted time window  X  10-4,  m2  M  10-5  Watts  c  10-6  B  10-7  A  10-8  2014-11-09T15:29:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='300  15:20  15:24  15:28  15:32  15:35  15:39  15:43  15:47  15:50  15:54  15:58  16:02  Universal TimeActiveRegion#11OBSID:3660105403  10-3  extractedtimewindow  X  10-4  m2  M  10-5  Watts /  C  10-6  B  10-7  A  10-81  00:35  00:40  00:45  00:50  00:54  00:59  01:04  01:08  01:13  01:18  Universal TimeA&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  number of bits required to decode a signal using an estimated  distribution rather than the true distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is also equivalent  to maximizing the log-likelihood of the data under {θ} and is  identical to the KL-divergence up to an additive constant, where  the KL-divergence is a pseudo metric used to measure the dis-  similarity/distance between two probability distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  With large datasets, it is computationally expensive to only  update the weights after computing the sum of the loss over ev-  ery training example (a single epoch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For this reason, we use  a variant of gradient descent called stochastic gradient descent  (Saad 1999), which updates the weights based on a pseudo loss  that is estimated by randomly sampling a subset of spectra in-  stead of all spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In our case, N only runs over 64 spectra for  each update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The last term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1 is not part of the definition of the BCE-  loss but is added to penalize the weights and help the model gen-  eralize to new data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is necessary since our true objective is  not simply to maximize the number of correct predictions with  the data the model was trained on, but to develop a robust model  that can correctly label new data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The prefactor λ is called a reg-  ularization parameter and dictates the trade-off between model  performance and robustness, with larger values generally leading  to poorer performance on the training set but better generaliza-  tion to new instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If we do not regularize the model, gradient  descent would most likely converge to a set of weights that are  overly optimized on the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To get a true measure of a model’s performance, it is impor-  tant to test the model with data that it has not encountered during  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is standard practice to therefore split the data into a  training, validation, and test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' While the weights are adjusted  using data from the training set, the hyperparameters such as the  model architecture as well as the regularization term λ are ad-  justed on the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The test set then serves as the gold  standard to judge a model’s performance and ability to general-  ize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The quality of the model can then be judged by analyzing  the behavior of the loss (or accuracy) as a function of epoch  (training time) on both the training and test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' During training,  these two losses trace out curves collectively known as learning  curves (as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2), whose joint dynamics can be used  to identify unwanted behavior such as under or overfitting the  training data, as well as the optimal training time (either red or  blue vertical lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The model with the lowest loss on the test  set is usually selected as optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  0  10  20  30  40  50  60  70  80  90  100  Epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='60  Loss  Learning curves obtained during training  best test  best av  train Loss  test Loss  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Example of learning curves obtained during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The black  and gray curves indicate the performance (in terms of loss) of a model  on both the training (black) and test (gray) set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The best model could  either be the model that scored the lowest loss on the test set (red dashed  line), or the average lowest loss on both the training and test sets (blue  dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Notice that after about 50 epochs the test loss starts to  increase, indicating a possible overfitting of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Convolutional neural network  Optimization problems such as these are commonly parameter-  ized by NN’s, meaning that the function FΘ is replaced by a NN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  A ConvNet is typically composed out of two sections as seen in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A feature extraction segment, inspired from the organi-  zation of an animal visual cortex (Hubel & Wiesel 1968), which  derives high level interpretable features via the use of stacked  convolutional modules (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2016), and the  classification segment, composed of multiple fully connected  dense layers that are responsible for interpreting those features  and mapping them to a binary classification output (AR/PF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For  a detailed description of the fully connected component see ap-  pendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  ConvNets provide several desirable advantages over sim-  ple fully connected networks, most importantly, they provide a  means to automatically search for useful features in the input that  may help minimize the loss function and lead to better classifi-  cations (LeCun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This implies that the convolutional  section of the network generates a potential set of "reservoirs"  for extracting explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Our particular ConvNet contains six  such reservoirs referred to as feature maps Ak, indicated by black  vertical lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each feature map is constructed via a suc-  cession of simple layered operations as indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Firstly, a filter/ kernel, sweeps across the input with a pre-  defined number of steps between each stride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this case, the  filter has a visual field of three units and a stride of one unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' At  each step, the network takes the dot-product of the input and the  kernel (a convolution), to produce the set of numbers seen in the  next layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is important to note that at this stage two critical  attributes are injected into the ConvNet that distinguish it from  its fully connected counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Firstly, each output node is con-  nected to only three input pixels, unlike a fully connected layer  where every neuron is connected to the entire visual field of the  input, and secondly, the parameters of the filter (in this example  scalar values [−1, 0, 1]) are reused for each convolution across  the entire input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This means that not only do we have fewer con-  nections between the layers, but those connections that we do  have are restrained to share similar sets of weights {θ}, resulting  in a drastic improvement in computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The output vector resulting from these convolutions is then  passed through a ReLU activation function which introduces a  nonlinearity by replacing any negative numbers by zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The  resulting feature map can optionally be further reduced in size  by applying a layer that extracts global statistics, such as a max  pooling layer that maintains the largest of two numbers when  sweeping over the feature map in strides of two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Pooling layers  such as these make the network’s output invariant to small shifts  or rotations in the input, since only general information across  multiple pixels is retained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, these layers help allevi-  ate overfitting and further reduce the number of parameters fed  into the fully connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Returning back to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3, each vertical black line represents  a feature map that has been obtained using a different filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The  values of each filter also contribute to the set of parameters {θ}  that define the network, and are updated in kind via backprop-  agation (a NN equivalent of gradient descent) in order to mini-  mize the loss function in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This means that each map tries to  identify useful features to serve as an optimal basis for the fully  connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  During training, the kernel of each feature map alters its pa-  rameters, in order to strengthen responses to particular input pat-  terns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For instance, one of the feature maps could be dedicated to  identify triplet emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If a spectrum has large triplet emission,  Article number, page 4 of 21  Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  max pooling  convolutional + relu  (240)  (2, 74)  (4, 22)  (4, 11)  (44)  (5)  (2)  fully connected  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Schematic of a ConvNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This network is a hybrid between a set of convolutional layers and a fully connected feed forward network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The  convolutional layers contain kernels that scan through the input and extract feature maps (vertical black solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each layer forms successively  more abstract and sophisticated maps, with each filter being sensitive to a particular feature that the network deems important for the classification  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The high level features which the network automatically generates are then passed through a max pooling layer (gray vertical lines), which  take summary statistics of the maps, reducing the number of parameters and promoting generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The final content is then fed into the fully  connected layers which behave as described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1, and are responsible for classifying the spectrum into either the AR or PF class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is  important to note that the weights and kernels are updated during training, meaning that the ConvNet adaptively searches for a set of features that  is most helpful for distinguishing between AR and PF spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Input Spectrum  Filter  Feature map  ReLU  Max Pooling  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Schematic for the generation of a single feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A fil-  ter/kernel consisting of a visual field of three pixels scans over the input  in strides of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' At each position, the dot-product between the input  and kernel is taken to form a single output in the next layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This pro-  cess is referred to as a convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The resulting output is then passed  through a ReLU activation function which introduces a nonlinearity into  the network by setting all negative values to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The feature map Ak  i  can then optionally be passed through a max pooling function, which  scans across the map in strides of two and maintains only the largest  value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The convolution process makes the network efficient by promot-  ing sparse connections and weight sharing, while the pooling layer fur-  ther reduces the number of parameters and promotes invariance of the  network output to small shifts and rotations of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  then this filter will become very active and initiate a strong sig-  nal to the fully connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 5,  which shows the actual activations of our trained network for  each feature map in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In order to see what feature each map  is searching for, we have projected the activations back onto the  input spectrum, with darker regions indicating importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The first convolutional layer contains two maps that differ  only slightly from the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These maps are then convolved  in the second layer to produce more abstract and sophisticated  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We can see that in the final layer, the feature map A1  has understood that the input spectrum contains triplet emission,  and furthermore, that this is important for the classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Map A3 on the other hand is searching for the presence, or lack  of pseudo-continuum emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We therefore see that the con-  volutional layers act as a type of translator, identifying the most  suitable language for the fully connected layers to interpret, and  Conv1  Conv2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Diagram showing the actual activations of each feature map in  response to an input spectrum x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These maps correspond to the 6 vertical  black solid lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Darker shades show what part of the spectrum  each map is identifying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  furthermore, that the final convolutional layer contain the most  sophisticated understanding of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1  The details of our ConvNet can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The raw  spectrum enters into the network, is convolved with two filters  that have strides of 3 and visual fields of 20 pixels each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The  convolved outputs are passed through a ReLU activation func-  tion to produce two maps of dimension 74 each (We note that  any remaining pixels after taking the modulus of the convolution  are dropped).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These two maps serve as inputs for the generation  of four more abstract maps that were obtained using filters of  stride 3 and visual fields of 10 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The contents of these fil-  ters are then reduced via a max pooling layer (stride 2 kernel size  2), flattened into a single vector of size 44, and then fed into the  fully connected layers for classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For reasons discussed in  section B of the appendix, this parameterization of the ConvNet  represents a minimalistic architecture that proves sufficient for  our classification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Explainable AI techniques  In this section, we briefly describe two different methods,  Gradient-weighted Class Activation Mapping (Grad-CAM) and  Expected Gradients (EG) for extracting features from Mg ii that  1 The spatial coherency seen in the feature maps is shattered when  passed through the fully connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Article number, page 5 of 21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  cs3-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='30  0c3A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  are important for flare prediction, while their detailed description  can be found in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Both of these methods are applied  to our ConvNet after it has been trained (post-hoc), and produce  visual explanations in the form of saliency maps, which are sim-  ple heatmaps that can be projected back onto the input spectrum  to indicate the most critical features that were responsible for the  network’s decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The most important features of an input are  often referred to as the discriminant region, because this is the  region that the network focused on to discriminate between the  PF/AR classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If the network was trained to distinguish between  spectra from active regions that did not lead to a flare, and active  regions that resulted in a flare, then the heatmaps will highlight  any hidden features of the spectral line that are particularly as-  sociated with preflare activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM  Since ConvNets are pattern recognition tools that store spatially  coherent high-level representations of the input within their fea-  ture maps, much work has gone into understanding and visu-  alizing the internal content of these special units (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Mahen-  dran & Vedaldi 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Dosovitskiy & Brox 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It was re-  cently demonstrated that the last layer of feature maps in a Con-  vNet have the ability to behave as object detectors when sim-  ply trained on binary classification tasks (Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Further research showed that the addition of a global pooling  layer (GAP) directly before the softmax classification layer, al-  lowed researchers to simplify the network enough to project the  weights of the feature maps back into the image space to ex-  tract the precise discriminant region responsible for a particular  classification (Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Their technique called class ac-  tivation mapping (CAM) had a distinct disadvantage in that it re-  quired an oversimplification of the models architecture to work,  which might lead to compromises in the performance of the net-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Gradient-weighted Class Activation Mapping (Grad-CAM)  (Selvaraju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2017) represents an improvement on CAM in  that it requires fewer architectural constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It has recently  been used to automatically identify important features in HMI  full-disk magnetograms for flare prediction (Yi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Grad-CAM evaluates the importance of the patterns identified  by the feature maps in the final convolutional layer, by monitor-  ing the effect that small perturbations to these maps have on the  output prediction score for a particular input spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A low  resolution saliency map is then constructed by taking a weighted  linear sum of the feature maps, with more weight assigned to  those maps that effect the output most.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The saliency map is then  extrapolated to the dimension of the input and projected back  onto the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' One weakness of Grad-CAM is that the qual-  ity of the explanation depends strongly on the selection criterion  of the network’s architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For a detailed description of this  method see appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Expected gradients  Expected gradients (EG) does not require special convolutional  layers, although the same network used to generate explanations  for Grad-CAM can be reused.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Instead of perturbing components  within the network to evaluate the importance of patterns, EG  works directly at the resolution of the input by removing pix-  els/wavelength points and evaluating the net effect on the pre-  diction score (Gabriel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To ensure the fair distribution  of pixel importance, EG makes use of a game theoretic quantity  call the Shapley value φi (Shapley 1951), which was originally  constructed to fairly distribute rewards over coalitions of players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Under this formalism, the importance φλ(FΘ) of a single inten-  sity point with the current model is obtained by calculating the  average difference between the prediction score under all combi-  nations of pixel coalitions with and without the pixel in question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Since this requires taking many subsets over the input, the for-  malism has to be adapted to be amenable for NNs, which require  information to be pumped continuously through each pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In-  order to generate pseudo-subsets, EG "turns pixels off" by flood-  ing them with information from the actual dataset, such that the  expected value from these pixels after many passes results in a  net-zero effect on the output prediction score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Unlike Grad-CAM, the saliency maps generated from EG are  often less smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since it is sensible to require that the variance  in importance between proximal pixels be small, EG can incor-  porate the attributions into the training procedure as a differen-  tiable prior that often leads to smoother saliency maps and faster  convergence (Gabriel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We however use the attribu-  tions derived in Grad-CAM as a guide for applying a post-hoc  smoothing after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For a detailed description of EG see  appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Testing our architecture and XAI  implementations on an artificial dataset  Only a few examples of attribution methods exist for one-  dimensional inputs such as spectra (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=', Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2016), we  therefore had to test our implementation of the ConvNet’s archi-  tecture and XAI methods in a controlled environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We note  here that both XAI methods returned similar results (as will be  shown in section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2), and as such, we only show the outputs  derived from Grad-CAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Our artificial dataset consisted of 700k randomly selected  Mg ii spectra from several solar flares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' From these spectra, we  constructed two classes, the first class was composed out of the  original flare spectra, while the second (positive) class consisted  of an identical copy of the first except for a small artificial pertur-  bation inserted at the center of each spectrum, as seen in the top  panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The task of the ConvNet is exactly the same as  our present task, namely to solve the binary classification prob-  lem of correctly labeling the class of each spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since both  classes are identical except for the perturbation, the only way for  the ConvNet to distinguish between spectra from the two classes  is to focus all of its attention on the perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  This is exactly what we see in the remaining panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 6,  which show how the ConvNet adjusts its focus during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  From top to bottom, each panel shows the heatmap derived from  the Grad-CAM procedure outlined in the previous section (EG  results are equivalent), with warmer colors (oranges, reds) rep-  resenting wavelengths that the network has deemed important  for its classifying task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The batch number associated with each  of the plots indicates how many spectra the network has trained  on (1 batch is equal to 240 spectra, and each batch represents a  single adjustment to the weights).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The weights of the network,  both in the fully connected layers and the six filters, are initiated  randomly, and as a consequence, the second panel indicates  that the network has not discovered any important features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  After batch 50, gradient descent has allowed the filters to start  identifying a portion of the central perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' With increasing  training time, eventually all of the network’s attention is focused  on the artifact, resulting in a classification accuracy of 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  This implies that 1) we have a satisfactory network architecture  Article number, page 6 of 21  Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM as a function of training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A single batch means  that the network has trained on 240 spectra from the artificial dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Initially the ConvNet focuses randomly on the left wing of the k-line  core, before pooling all of its attention onto the artifact, resulting in a  classification accuracy of 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM allows us to deduce that  the most important feature for the network’s decision making was ex-  clusively the artifact, which by design was the only way to distinguish  the two classes of spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  at least for solving simple problems, and 2) that our attribution  method highlights the feature that distinguishes the two classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  There is however an important caveat which is not explored  by this example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' As it turns out, once the network has discovered  a portion of the artifact its classification score saturates rapidly,  and there exists very little motivation for the network to further  adjust its weights to make the perturbation its central focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This  results in saliency maps (as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 7) that highlight residues  of unimportant features, such as the h&k-line cores, and partly,  or asymmetrically cover the artifact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To be clear, the saliency  maps shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 7 were derived from fully trained ConvNets,  which in both cases performed perfectly on the classification  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM after two separate training runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Both figures show  saliency maps derived from fully trained ConvNets on the artificial  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In both cases, the models achieve near perfect classification  scores, however, the central artifact is asymmetrically covered by the  network’s attention, and residual unimportant features such as the line  cores still show nonzero contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The problem here can possibly be attributed to a flat/wide  global minimum within the loss space as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In  this hypothetical loss space, each of the white circles represent  a convergent set of parameters {θ1, θ2} found by training differ-  ent randomly initiated models via gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Although  each converged white circle represents an optimal solution given  the loss function L(θ), such as those found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 7, it does  not represent the optimal or most intuitive explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In other  words, when trying to derive explainable solutions we are forced  to solve two optimization problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The first is simply the loss  given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1, which promotes accurate predictions, while the  second loss is harder to formulate and represents the solution that  delivers the maximum amount of explanatory power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Given the  simple configuration of this test, we know that the best expla-  nation is to have the network symmetrically highlight only the  central artifact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This would represent the solution at the center of  the well in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Since the meaning of "explainable" is not easily formulated  mathematically, we cannot construct an additional term in the  loss function that gives the ConvNet a set of instructions to auto-  matically transverse the degenerate space of solutions towards its  center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We can however locate the center by means of a Monte  Carlo approach, by taking advantage of the randomness of the  initial states, and then appealing to the law of large numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Our course of action is therefore to generate a "swarm" of mod-  els, whose solutions populate the perimeter of the degenerate  minima, and then take the average saliency map of the entire  ensemble  ¯Mc =  �  Θ∈Ω  (FΘ → Mc)/|Ω|,  (2)  where FΘ as usual is our function parameterized by a ConvNet  with unique weights Θ, and Mc is the attribution map produced  by a particular model under the Grad-CAM formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The final  weight solutions are part of a larger set of possible weights Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The results of this method which we call the ensemble method,  can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Although the line cores still occupy a residual focus of the  network, the central minimum is indeed the focus of attention  Article number, page 7 of 21  Attention of ConvNet during training  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  Batch: 70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  Importance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Schematic indicating the problem of obtaining the optimal solu-  tion both in terms of model performance and explanatory power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The x-  and y-axis represent the parameters of a fictitious two parameter model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Adjusting the model parameters affects the loss, which we ideally want  to minimize (lighter regions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Gradient descent allows us to converge  to the global minimum in a controlled manner, however, there might be  multiple solutions (as indicated by the white circles) that have the same  loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Although these points are degenerate in terms of model perfor-  mance, they do not all have the same explanatory power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We postulate  that the best explanation is located at the center of gravity of this de-  generate space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This point must be located stochastically by initiating  several models and then taking the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM results after averaging over an ensemble of fully  trained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Although the residual attention in the cores has not  fully drained to the artifact, taking the average saliency map from multi-  ple converged runs results in a symmetric covering of the perturbation,  indicating that the ensemble method offers a possible mechanism for  identifying the most intuitive explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  and symmetrically covered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The unwanted attention attributed to  the cores (as seen by the turquoise coloring) can possibly be re-  moved in several ways 1) by including more models into the en-  semble, 2) by using a smart optimizer such as Stochastic Weight  Averaging (SWA) (Izmailov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2018) that allows the solution  to stochastically wander around the central minimum before tak-  ing the average of the model weights, or 3) by implementing a  sort of annealing by randomly perturbing the weights around the  minimum and reducing the importance of those weights which  affect the model’s accuracy least.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We selected the first option of  including more models, although this is computationally more  expensive, it has the least amount of unknowns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It should also  be pointed out that in effect, the attribution prior (and less so the  post-hoc smoothing) used in EG and discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2, is  an attempted mechanism for traversing the degenerate minima  to the center of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  In conclusion, the need for explainable models places a  precedence on the degenerate solution space, since although all  solutions have the same performance, they do not have the same  explanatory power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We make the assumption that the optimal so-  lution, both in terms of performance and explanation, is located  at the center of gravity of the degenerate minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Due to the  nonmathematical formalization of "explanation," this center of  gravity cannot be searched for via controlled optimization tech-  niques, but must be located stochastically via a Monte Carlo ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is not clear to what degree the problems encountered  here carry over into the real AR/PF dataset, however, we expect  that the loss surface will not be as degenerate, allowing the resid-  ual attention to naturally drain with increased training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Fur-  thermore, it is difficult to imagine why the tenants and practices  derived here would not hold in more complex scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Creating train and test sets  Our data, as well as the objective of obtaining not only high  performance classifiers, but also explanations from our network,  complicates the training procedure outlined in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The last section has clarified that we need to train multiple  randomly initiated models simultaneously to derive the most  intuitive set of explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Although we remain true to the  general tenants already outlined, such as minimization of our  loss function and splitting our data into a training and test  set, it is not immediately obvious how one selects the data  that should be in each of these sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We also note that we do  not optimize our model’s hyperparameters with the intent of  increasing performance metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This implies that a validation  set is unnecessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this section, we explain the method and  logic behind our particular choice of data partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Our main objective is not simply to discover that spectra  from a single PF region are different from spectra from a sin-  gle AR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This might be the case, but it also might simply be a  peculiarity of the two selected observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In such a circum-  stance, the results would not serve our purpose of understanding  general flare precursory behavior, and would represent a type of  overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We instead wish to extract only those differences that  persist over many observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is clear then that we require  many IRIS observations, and furthermore, that we test the model  on data that was not used during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, to avoid  another potential form of overfitting, spectra from the same IRIS  observations cannot be both in the training and test sets, since  the models could then learn particulars about the observations  themselves, thus suppressing the model’s ability to extract gen-  eral precursory flare behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To decide how to partition the 19 PF and 18 AR observations  into two sets, we had to make an experimental design decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1)  We could either randomly partition the observations, 2) perform  a computationally expensive k-fold validation technique which  averages over many partitions, or 3) select the partition that leads  to the highest model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We dismissed the first option  on the grounds that it could result in an unfortunate partitioning  given the low number of observations, thus flooring the entire  experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The second option, although thorough, is extremely  computationally expensive and has the potential of suppressing  common preflare signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The computational costs of this op-  tion can easily be appreciated if we consider that for every fold,  one has to train multiple models to obtain optimal explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  These models then need to generate a collection of saliency maps  at a nonnegligible expense that are then averaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These aver-  aged maps themselves have to be averaged over all k-folds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We therefore selected the third option based on the follow-  ing logic: If a common flare triggering mechanism exists and is  Article number, page 8 of 21  Optimal explanation  Flat global minimum  Gradient descent  Degenerate solutions  01Grad-CAM for positive classification  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  Importance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  noticeable in the UV, then it would be presumptuous to expect  that it exists in every observation, and furthermore, even if it  did, IRIS’s slit may sometimes miss the preflare signatures ow-  ing to its limited field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Therefore, to give our models the  best chance of isolating a frequent preflare signature, the parti-  tioning that leads to the highest model performance would likely  coincide with a partitioning that divides observations with this  mechanism into both sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To determine this optimal partitioning, we trained the Con-  vNet in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3 for 50 random splittings of observations, assign-  ing 5 AR and 5 PF observations to the test set and the remaining  observations to the training set for each split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since each obser-  vation contains a different number of spectra, we ensured AR/PF  balance by undersampling the majority class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We note that mis-  representing the natural frequency of the classes could result in  an inflated false positive rate (Woodcock 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Bloomfield et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Deshmukh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2022), however, we found no significant  effects due to undersampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We also enforced a 3/2 split for  the final training and validation sets, meaning we had 50% more  data for training than testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For each of the 50 splits, we al-  lowed the ConvNet to train over 100 epochs and for each case  extracted the model with the lowest loss on the test set, as seen  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The statistics for the TSS scores of all 50 partitions can  be seen in the boxplot of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 10, which shows that the models in  general perform skilfully on the binary classification task (a TSS  > 0 is better than a random guess).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We then selected the partition  corresponding to the red dot, which resulted in one of the highest  TSS scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We note that the number of spectra contributed by each ob-  servation although similar is not identical, with some observa-  tions contributing more than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To ensure our models were  not biased to a particular set of observations, we tested their per-  formance when iteratively removing single observations from  the training and test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We noted little change to the overall  TSS, which supports the generality of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Training a swarm of models on the partition  The high TSS score associated with the chosen data partition  in the last section increases the chance that the model learns a  meaningful and common set of preflare signatures that is worth  extracting using our XAI techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' From section 5, we know  that the optimal explanation is most likely obtained using Monte  Carlo methods by training a large number of models in concert  and then taking the average attributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We therefore trained  a 50 model ensemble on spectra from the training set, with all  models achieving TSS scores around ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8 on the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Downsampling the swarm  Applying the full 50 model ensemble to each spectrum of  the combined PF/AR dataset is computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We  therefore manually selected a subsample of 9 models that best  preserved the average attributions/heatmaps of the entire swarm,  resulting in drastic reductions to the computational time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To test  the validity of the reduced model selection, we ran tests over  several hundred randomly sampled spectra, and compared the  heatmaps derived from the full 50 model swarm and those de-  rived from the 9 representative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We noted little to no  loss of explainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The perceived continuity of generated  heatmaps under a smart subsampling of models can be inter-  preted as selecting a minimum of critical points that when av-  eraged result in a point at the center of gravity of the loss land-  scape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For instance, if the loss function was that seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 8,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='9  TSS  TSS for all 50 partitions  all other splits  selected split  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Boxplot of the ConvNet’s performance in TSS for all 50 random  partitions of the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The red mark represents the performance  of the selected model, while the blue dots are the scores from the re-  maining partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The vertical red line is the median score of all splits,  while the edges of the gray box outline the first and third quartiles, the  whiskers at the end denote the min and max values while anything out-  side of this limit is considered to be an outlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The plot shows that the  model easily achieves a high skill on the binary classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions derived using Grad-CAM (top) and Expected Gra-  dients (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Both techniques are equivalent up to an additive con-  stant as they highlight the spectrum in a similar way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this case, the  model indicates that red wing enhancements are important signs of im-  pending flares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  then one could achieve the same result by densely populating the  circumference of the minimum with many models, or just sim-  ply two critical models whose parameters converge to positions  opposite one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Equivalence of Grad-CAM and EG  We now investigate whether the Grad-CAM and EG formalisms  are equivalent, in other words, whether the vector that both meth-  ods produce are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Figure 11 shows a spectrum taken from  the PF dataset and fed through the ensemble of representative  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The upper and lower panels show the derived model at-  tributions (colors) using Grad-CAM and EG respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Both  Explainable AI techniques highlight the spectrum in a similar  way, however, the heatmap from Grad-CAM has been scaled  up by an additive constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The similarity between attributions  across techniques appears consistent over different samples of  spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We therefore conclude that the Grad-CAM and EG tech-  niques are equivalent for our purposes up to an additive constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  In this particular case, it appears that the explanation is not opti-  mal since the ConvNet focuses most of its attention on the k-line  for its decision rather than distributing the importance evenly  over both cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This may be a consequence of the high degree  of symmetry between the line core shape, such that is the net-  Article number, page 9 of 21  Grad-CAM for PF spectrum  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  LD  Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='D  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)EG for PF spectrum  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  LD  Intensity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Four spectrograms (labeled A-D) in black and white and their associated saliency maps as calculated using Expected Gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Darker  shades in the spectrograms indicate higher intensities, while warmer colors, such as reds and oranges in the attribution maps are linked to features  that the model believes are important for flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each attribution map was normalized such that their colors are comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The position  of the h&k-line cores, as well as the red wing subordinate line are indicated by horizontal black dashed lines in the attribution maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Panel A  through D shows that triplet emission, downflows, broad line cores, and highly asymmetric spectra respectively, are indicative of forthcoming  flares according to the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  work need not analyze both cores for its decision as discussed in  section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We do however stress that these explanations are lo-  cal, meaning they are particular to each spectrum, and that many  times the network does treat the cores on an equal footing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Having established this equivalence we decided to use EG  for the remainder of the analysis because of its favorable ax-  iomatic property of completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This property states that  �  λ φ(xλ) = FΘ(x), that is, the sum of attribution values across  a spectrum’s wavelengths is equivalent to the prediction score of  that spectrum after being passed through the ConvNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This al-  lows us to create an equivalence between integrated attributions  and prediction scores effectively folding the one onto the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  It also means that attributions are only useful at the scale of the  wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Results and discussion  In this section, we present the results of applying our ConvNet  and XAI methods to the AR/PF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' After processing the data  each spectrum becomes associated with 1) a single scalar value,  which is the ConvNets prediction score ˆy indicating whether it  believes the spectrum is from the PF class (closer to 1), or the  AR class (closer to 0), as well as 2) a vector which redistributes  the total prediction score across the spectrum, functioning as our  heatmap to indicate which features are most responsible for the  total score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We then analyze these outputs at several progres-  sive resolutions, firstly at the level of single spectra and spectro-  grams, then across the IRIS slit in time, and finally over entire  observations in relation to the flare start time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions over single spectra and spectrograms  In order to quickly analyze what the model found important  throughout the entire dataset, we compiled each spectrum into a  compact representation known as a spectrogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Spectrograms  are concatenations of single spectra in time along pixels from  IRIS’s slit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Four examples of spectrograms can be seen in the  black and white images of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We note that a single verti-  cal slice from a spectrogram corresponds to a single spectrum,  whose shape is encoded as an intensity map (darker here means  more intense).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This compactification left us with 59026 PF and  33316 AR spectrograms instead of millions of single spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We then ordered the spectrograms according to their mean pre-  diction scores and manually scanning through the results with  the highest scores, that is, those spectrograms that were strongly  associated with flare precursory activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Within these spectro-  grams we found consistent patterns that are well represented by  the four examples shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Each of the four panels labeled A-D consist of the original  spectrogram (with darker colors indicating more intense emis-  sion) and its associated saliency map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The saliency map con-  sists of stacked single spectrum attributions like those in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The y-axis (left) is always wavelength (measured in Angstroms)  while the x-axis is the raster number of the original IRIS obser-  vation, which implicitly encodes time as a function of the raster’s  cadence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For clarity, a minute interval is demarcated by a black  horizontal line in the attribution maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since all of these observa-  tions span 25 minutes and terminate with a solar flare, the lengths  of the markers are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The y-axis (right) tracks the pre-  diction score which is traced out by white lines in the saliency  maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The position of the vacuum Mg ii h&k-line cores as well  as the red wing triplet emission are demarcated by black dashed  horizontal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The scores and attributions are encoded into the attribution  maps as follows: The average score assigned to each spectrum  (at each raster) from the ensemble of representative models en-  codes the transparency of the map, such that darker regions are  seen to be more important for flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' EG then takes  Article number, page 10 of 21  Obs:20140611181927.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3863605329,  Slit Position: 3, Pixel:100  A  2796  Wavelength  2798  Intensity  2800  2802  2804  Expected Gradients  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='00  A  2796  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='95  Wavelength  2798  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='90  2800  At = 1min  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='80  2804  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='70  360 365370375380 385390395400405410415420  425  IRISrasterObs:201503110446033860259280,  Slit Position:4, Pixel:535  B  2796  Wavelength  2798  Intensity  2800  2802  2804  A  ExpectedGradients  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='95  tance  Wavelength  2798  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='90  2800  △t=1min  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='85  2802  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='75  2804  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='70  94  96  98  100  102  104  106  108  110  112  114  IRIS raster0bs:201506221700033660100039,  Slit Position: 5, Pixel: 162  c  2796  2798  Intensity  2800  2802  2804  ExpectedGradients  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='00  A  2796  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='95  tance  Wavelength  2798  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='90  2800  At = 1min  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='85  2802  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='80  2804  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='70  IRIs rasterObs:201402122154583860257280,  Slit Position:4,Pixel:434  2796  D  Wavelength  2798  Intensity  2800  2802  2804  ExpectedGradients  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='00  A  2796  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='95  tance  Wavelength  2798  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='90  2800  At = 1min  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='85  2802  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='80  2804  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='70  IRIS rasterBrandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  these raw scores and fairly distributes them across the wave-  lengths turning scores into attributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Regions of high attribu-  tions are colored with warmer colors and indicate those features  which are seen as important for flare forecasting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' All panels were  normalized with an arbitrary value to make their respective col-  ors comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions of individual spectra associated with the saliency  maps in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each spectrum is a slice from the attribution maps  from the locations indicated by the vertical dashed red lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The y-  axis is normalized intensity and the x-axis is wavelength in angstroms  (Å).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Red, orange and turquoise colors indicate features that the model  associates with precursory flare activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Panel A shows that triplet emission is strongly indicative of  preflare activity, since EG highlights the portion of the spec-  trogram (in red) where this emission can be seen to become  enhanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' When the triplet emission subsides, the model’s at-  tention synchronously dissipates (colors turn from red to blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Similarly, panel B indicates that velocity flows in the form of red  wing enhancements are also indicative of preflare activity as can  be seen starting around raster 112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is important to note that up-  flows are regularly flagged as important but are not shown in the  figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The spectra in Panel C appear to become substantially  broader around raster 44, and are consequently highlighted or-  ange and red, indicating a positive relationship between preflare  features and broad spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Finally, panel D shows extremely  broad asymmetric spectra that are flagged as strong predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  An example spectrum from each panel can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 13,  each of which were extracted from their corresponding spec-  trogram from the locations indicated by the red vertical dashed  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We note that the prediction scores, as traced out by the white  lines in the attribution maps of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12, are saturated close to  the maximum PF prediction score of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is because these  maps represent some of the highest scoring maps in our dataset,  while other maps scored much lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions over IRIS slits  The location of high attributions (warm colors) within the 25  minute windows of each saliency map appear to be randomly  distributed, and do not display a monotonic increase in predic-  tion score closer to flare onset as was found for the case of the  X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6-class flare observed by IRIS on 2014 September 10 (Panos  & Kleint 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It is important to note that for the September  10 event, the authors restricted the pixels of the sit-and-stare to  those associated with enhanced activity within the SJIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To con-  clude whether or not there is any general tendency for prediction  scores to increase during flares, we have to integrate over the  entire IRIS slit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Figure 14 shows two positive instances that demonstrate ap-  proximate monotonic increases in prediction score with time (for  a comparison with nonflare events see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Here we have  taken the mean attribution score of each spectrum, that is, we  integrated over wavelengths to produce saliency maps over the  entire IRIS slit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The black and white panels indicate the intensity  along the slit at different times with darker colors being more in-  tense than lighter colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The black curves show the GOES X-ray  flux with flare class indicated on the y-axis on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Below  each of these images are their associated saliency map which as  usual indicates the most important regions along the slit in time  using the same color code (warmer colors are more important  for prediction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The white curves indicate the prediction score in  time integrated over all pixels, not just a subset that was used  in (Panos & Kleint 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The upper left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12 is in-  fact a spectrogram taken from a single pixel of the upper panel  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14, while the lower panel is of a new PF observation en-  tirely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The vertical black line indicates the end of the PF period  and the start of the flare according to the GOES catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The in-  tensity and attribution maps were normalized separately across  both sides of this divide, to ensure that the details of the PF pe-  riod were not drowned out by the relatively much higher intensi-  ties and attributions during the flare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We find that in roughly 105  out of 135 slits from the 19 PF observations, the location of the  maximum attribution along the slit is predictive and aligned with  the maximum UV emission later during the flare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Another good  example of this can also be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2 in the supplementary  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  In both cases shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14, we see that there is a gen-  eral tendency for high prediction scores to be associated with  enhanced intensities, even though the intensities are only implic-  itly encoded into our models after the normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If an ener-  getic event occurs within the chromosphere, the excess emission  from the line cores typically vastly outcompete the gains in the  continuum, leading to a pseudo continuum that appears flat after  normalizing the spectra by their maximum values, see section 2  for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To examine the relationship between intensity and prediction  score in more detail we plotted the mean attribution score of ev-  ery PF spectrum as a function of DN’s per second in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Larger average attributions imply spectra that the model be-  lieves is more useful for flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In the high intensity  regime right of the dashed orange line, the intensities appear to  Article number, page 11 of 21  EG for single spectrum from spectrogram A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6  Tormalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)EG for single spectrum from spectrogram B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='2-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)EG for single spectrum from spectrogram C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='2-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)EG for single spectrum from spectrogram D  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions over IRIS slits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The top panel shows an intensity  map (black and white) over the pixels of one of IRIS’s slit positions in  time, with darker colors indicating more intense emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The corre-  sponding saliency map can be seen below, with warmer colors (orange,  red etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=') indicating regions that are seen by the models to be important  for flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The black curve in the intensity map corresponds to  the GOES-curve whose flare level is indicated on the right axis, while  the white curve in the attribution map is the mean prediction score as a  function of time along the slit (score seen on the right axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The bottom  panel is the same but for a different observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Both examples have an  increasing prediction score closer to flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  be positively correlated with the attributions, with higher inten-  sity spectra being associated with higher attributions, however,  towards the "low intensity" regime, the coupling between attri-  bution score and intensity is only weak to nonexistent, and it is  possible to have low intensity spectra that are critical for flare  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Global explanations  Because the explanations derived from Grad-CAM and EG are  local, that is, specific for each spectrum, we aim to derive global  explanations so that we can investigate PF features in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To  do so, we evaluated the distribution of attributions for the high-  est scoring PF spectra, that is, those spectra that had prediction  scores between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='9 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We then determined the position and  magnitude of each spectrum’s maximum attribution score and  summed the results, allowing us to track the aggregate impor-  tance of each wavelength for the model’s decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The result-  ing distribution can be seen in the top panel of Fig 16 together  with an arbitrarily scaled PF spectrum (red) and active region  spectrum (blue) for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The vertical dashed lines mark the  position of the Mg ii h&k line cores as well as the Mg ii triplet  emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The histogram makes it clear that in general, the model  focuses on regions to the left and right of the k-core, with some  attention given to the cores themselves, the triplet emission, as  well as three metallic lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This offers statistical support for the  observational claims made in section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1 in relation to Fig 12, in-  dicating that features such as triplet emission, flows in the form  of red and blue wing enhancements, as well as broad cores all  contribute positively to the network’s prediction score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The large  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Scatterplot of the average attribution using (EG) for each spec-  tra in the PF dataset as a function of intensity (DN/s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The plot is divided  into a low and high intensity regime by a dashed vertical line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The red  lines in either regime represents the best linear fits, and the correspond-  ing R2 values are provided in the upper part of each regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We see  that "low intensity" spectra can still be critical for flare prediction, and  that very high intensity spectra are more strongly correlated with higher  prediction scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  focus given to wavelengths on the left of the k-core is not ex-  clusively due to upflows, with the model also using these wave-  lengths to identify broad spectral cores such as those indicated in  the third panel of Fig 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In fact, upon visual inspection, down-  flows are far more prominently given attention than upflows in  our dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The model appears to also place focus on particular  absorption lines in the pseudo continuum corresponding to  Ni i, Cr ii, and Mn i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To explain the model’s focus on these  metallic lines, we randomly plotted many samples of spectra  that coincided with high attributions around these wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We found no evidence of emission in these lines, however, we  know that the continuum height acts as a proxy for intensity  (high intensity leads to flat continuum after normalization)  and therefore we assume that the model uses these absorp-  tion lines to determine the "flatness" of the continuum and  thereby the intensity of the spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is supported by a PF  observation where the highest attribution scores of the models  are clustered around the metallic lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An example spectrum  and its associated attributions is shown in the lower panel Fig 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Interestingly, the second panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14 shows large in-  creases in attributions from pixels 50−100 towards the end of the  PF period where the GOES curve is relatively flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Something to  note is the decrease in prediction score, which went from maxi-  mum values of 1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 12, to values around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This  decrease in prediction score is a direct consequence of integrat-  ing over the entire slit, where many of the slit’s pixels are sam-  pling inactive regions of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The dependence of the score on  arbitrary integrations shows that under this current framework,  we have to reevaluate our metric and method of predicting flares  in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Article number, page 12 of 21  Observation:201406111819273863605329,SlitPosition:3  200  150  Intensity  Pixel  100  M  50  0  200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='56  ExpectedGradients  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='52  150  tance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='48  Pixel  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='40  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='32  0  360  368  376  384  392  400  408  416  424  432  440  448  456  464  472  IRIs rasterObservation:201406121109333863605329,SlitPosition:4  200  150  Intensity  Pixel  100  M  50  0  200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='56  Expected Gradients  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='52  150  tance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='48  Pixel  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='40  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='32  0  1088 1096 1104 1112 1120 1128 1136 1144 1152 1160 1168 1176 1184 1192 1200 1208  IRIS raster0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='06  R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='002  R2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='261  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='03  (EG)  Score (  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='01  Mean Attribution  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='05  0  300  600  900  1200  1500  1800  2100  2400  Intensity (DN/s)Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Global explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Upper panel: Distribution (black bars)  showing where the model focuses most of its attention on aggregate  for the spectra that have high prediction scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For context, a red and  blue spectrum from the PF and AR class have been plotted respectively,  with vertical black dashed lines indicating the positions of the line cores  and triplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Flows that show up left and right of the k-core are important  as well as emission in the triplet line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Bottom panel: The model focuses  on the metallic absorption lines as a proxy for intensity, since intense  spectra after being normalized lead to flat pseudo continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Monotonicity  The problem of flare prediction is best framed as a two part prob-  lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The first part is relatively insensitive to the time domain,  and is only concerned with the performance of a model on a bi-  nary classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This is the approach that the majority of  flare literature addresses, and it is not principally concerned with  how these data are distributed in time or at what point within the  time window the flare will occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The second part concerns itself  with how the prediction score evolves over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The identifica-  tion of monotonic trends in features and or monotonic increases  in predictions are key to deploying practical flare forecasting  strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  One can imagine a scenario where triplet emission is critical  for distinguishing two classes (AR/PF) because this emission is  high for all PF observations and low for all AR observations,  however, it might be the case that the triplet emission, although  a greater indicator of class, does not significantly vary within the  PF observations themselves, so that it has a very weak predictive  utility along the time dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In summary, we need to iden-  tify features that not only tell us if a flare will occur, but also  when it will occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' There is also no a priori reason to believe that  these two sets of features need be the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions over entire IRIS rasters  Following the above discussion, it is also possible for the IRIS  slit at a particular step during the raster to be positioned off of the  active region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' When this happens, the prediction score does not  monotonically increase, but can randomly fluctuate and even de-  crease with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' By calculating scores in intervals averaged over  each raster of IRIS, we can set a fair baseline prediction for each  observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since this average score is arbitrarily predicated on  the active region itself as well as IRIS’ coverage of the region,  the baseline of one observation is not comparable to the base-  line of another observation, however the trends of the prediction  curve in time as well as its inclination do become comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Figure 17 condenses the behavior of our entire PF (top panel)  and AR (bottom panel) dataset within a single figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The upper  panel shows a heatmap, where the y-axis indicates PF observa-  tion, whose number corresponds to Table A1, and the x-axis is  time in minutes before flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Again the warmer colors indi-  cate periods of time that are seen by the models as important for  predicting flares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In other words, redder colors imply stronger  warning signals that a flare will occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To derive these heatmaps, each flare observation was placed  on a uniform time grid with intervals of 1 second and spanning  the PF period of 25 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A matrix of size (19×1500), corre-  sponding to 19 PF observations and 1500 seconds, was then in-  crementally populated with the average prediction score over an  entire raster for each observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Since most observations typi-  cally have cadences of more than two seconds, the initial high ca-  dence grid (and corresponding matrix) was only sparsely popu-  lated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Missing values were then filled in by linearly interpolating  across the calculated scores within each observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each of the  19 rows of the matrix were then normalized by their maximum  value so that observations with relatively high baseline predic-  tion scores did not drown out the behavior of prediction curves  from observations with lower baseline scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Furthermore, the  observations were purposefully ordered both within Table A1  and the matrix, such that observations with similar normalized  prediction curves would appear close together, thus aiding the  identification of patterns across the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The exact same steps  were also carried out for the AR observations seen in the bottom  panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We note that the PF dataset shows much more structure than  its AR counterpart which appears to have normalized predic-  tion curves that randomly evolve with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The PF observations  as seen in the upper panel, can be divided into two regimes (a  strong and weakly predictive regime) depending on the behavior  of their prediction curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Above the black horizontal line, we  see that 13 of the 19 observations tend to have prediction curves  that increase as we approach each observations flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Fur-  thermore, the prediction envelope with time smooths out as we  move down from PF observation 1 to 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Below the horizontal  black line we have six PF observations that do not appear to dis-  play any coherent behavior with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  To understand why some flares are easier to predict than oth-  ers, we analyzed the SJI and AIA movies in every available pass-  band for all PF observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We found that within the strongly  predictive regime, either the span of the rasters or the position  of the sit-and stares covered a region that was associated with  small brightenings as seen in Fig 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In contrast, many observa-  tions within the weakly predictive regime had poor coverage of  the major preflare activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, in the high prediction  regime, 77% of observations were large rasters (10 of 13 obser-  vations) with only 3 sit-and stare observations, this is in contrast  to the low prediction regime where only 33% (2 of the 6 ob-  servations) were rasters, implying that more spatial coverage of  the active region could lead to more reliable increases in predic-  tion score with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Furthermore, as indicated in the bottom two  panels of Fig 18, those sit-and-stares that were in the strongly  predictive regimes had the IRIS slit positioned directly over the  regions of most preflare activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Our small sample also appears  to indicate that M-class flares are easier to predict than X-class  flares, however, this could simply be due to the way these obser-  vations were sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A notable exception is the X-class flare  on March 29, 2014 (PF obs 14), which despite having excel-  lent coverage from IRIS nevertheless had a prediction curve that  decreased before flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The flare was possibly triggered  by an erupting filament which showed increased chromospheric  Article number, page 13 of 21  Global maximum attributions  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  scores  PF spectrum  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  AR spectrum  Attribution  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength [A]Metallic lines used as an intensity proxy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  Mn I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6  Cr I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  Ni I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2794  2796  2798  2800  2802  2804  2806  Wavelength (A)A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Attributions for all observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The top and bottom panel indicate the variation across all pixels and rasters of the models prediction score  with time for all PF and AR observations respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each row is normalized by its maximum value, and corresponds to a single observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Higher relative prediction scores are indicated by warmer colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We see that the PF observations (top) are much more structured and tend to  predict flares more strongly closer to flare onset, while the AR scores (bottom), result in a heatmap that is far more sporadic in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The numbers  on each panels y-axis correspond to the observation numbers listed in Table A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Doppler velocities at least an hour before flare onset, as well as  plasma heating 15 minutes prior to the filament eruption (Kleint  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A possible explanation for the poor predictive per-  formance, despite the good IRIS raster coverage and physical  precursory activity, is that spectra sampled from the filament are  out of the models learned distribution, since the filament erup-  tion is rare in the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Furthermore, the prediction  curve might be saturated in the 25 minutes analyzed and might  therefore drop to lower values further away from flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Conclusions  We applied a powerful visual network known as a Convolutional  Neural Network to IRIS Mg ii spectra with the objective of find-  ing differences between spectral shapes sourced from preflare  regions and active regions that did not lead to a flare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Our model  was capable of distinguishing spectra from both these classes  with a TSS around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8, and a large variance depending on how  the training and testing datasets were split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We then obtained visual explanations using two comple-  mentary explainable artificial intelligence techniques called  Gradient-weighted Class Activation Mapping and Expected Gra-  dients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These techniques allowed us to automatically discover  which features of individual spectra were seen by the model to  be most important for the task of flare prediction, representing  the highest possible resolution of explanations on the level of  the individual wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The techniques accomplished this by monitoring the sensi-  tivity of the predictions to either small variations within the net-  work’s internal components, or variations over input pixels di-  rectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In both cases the techniques returned similar results up  to an additive constant, and allowed us to project heatmaps onto  the spectra, with warmer colors (reds, oranges, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=') indicating  more important features than cooler colors (blues) for flare pre-  diction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' These heatmaps could then be applied to spectrograms  of IRIS in-order to automatically highlight critical regions that  could possibly indicate a flare triggering event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We found that in addition to high triplet emission and core  intensity, irregularly shaped profiles, broad spectral cores, and  single peaked spectra, flows in the form of extended red and blue  wing emissions were also consistently flagged by the model as  important precursory features, and that 78% of the time, high at-  tribution scores along the IRIS slit were predictive of the location  of the flare’s maximum UV emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The possible importance of increased turbulence as an early  warning sign and potential flare triggering mechanism has been  noted in the literature (Harra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2001), with an example of  a rise in nonthermal velocity taking place 11 minutes before  flare onset, possibly stimulated by rising flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Furthermore, even  though high scoring regions are typically associated with en-  hanced intensities, there are several instances where prediction  scores increase while both intensity and the GOES-curve remain  constant, once again consistent with the findings of Harra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Article number, page 14 of 21  increasing probability  Re  decreasing or random probability  25  24  21  20  19  18  17  16  11  10  8  Time before flare onset (min)RelativeImportance  18  6  7  8  9  10  11  1213  14  15  16  17  18  19  20  21  22  23  24  25  Time from start of observation (min)Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Selected images of different PF observations in the strongly pre-  dictive regime of Fig 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The PF observation numbering corresponding  to Table A1, as well as the filter wavelength is indicated in the top left  and right hand corners of each image, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The green vertical  lines indicate the span of the IRIS raster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The flares that are easiest to  predict based on spectra have the slit directly over regions where bright-  enings occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  (2001), and indicating the importance of spectral analysis for  flare prediction at a high resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We note that any practical deployment of a flare prediction  strategy for small field of view spacecrafts like IRIS with mul-  tiple programmable observational settings (exposure time, ca-  dence, raster mode etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=') is unlikely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The reasons for this are as  follows: If we use the prediction score (number of spectra scored  confidently by the network as PF), as a "flare warning signal,"  then the absolute value of the score becomes meaningless due to  arbitrarily variations in active region coverage, which depends  on the size of the active region itself, as well as programmatic de-  cisions such as IRIS’s slit length and area spanned by the raster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  All these free variables can either artificially drive the prediction  scores up or down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Additionally, features that were important  for the binary classification task of separating AR/PF spectra,  are not necessarily equally important for telling us when a flare  will occur in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' All these considerations imply that the ac-  tual objective for IRIS spectral based flare prediction, is not to  achieve high TSS scores, but to identify monotonically increas-  ing predictions that have steep inclinations, while disregarding  the absolute value of these curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We found that on aggregate, the prediction curves increased  for the majority of our PF observations closer to flare onset, how-  ever, there were several exceptions that did not show any coher-  ent increase in prediction score, and some observations whose  scores actually decreased in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An extensive analysis of each  PF observation over all SJI and AIA filters revealed that flares  were easier to predict when IRIS sampled a large spatial region  or had its slit positioned directly over small brightenings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Although practical and reliable flare prediction with IRIS is  unlikely, the methods developed here could easily be exported to  new instruments that can extract spectroscopic data from entire  active regions with multi-slit girds, such as NASA’s new MUSE  mission that has a multi, 37 slit EUV coronal spectrograph  (Pontieu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' All ConvNets and XAI techniques were programmed us-  ing the deep learning library of PyTorch (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019) and TensorFlow  (Abadi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For the implementation of the k-means algorithm, we used  the Scikit-Learn module (Pedregosa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The pre-processing was accom-  plished with IRISreader, a library specifically developed for handling large vol-  umes of IRIS data (Huwyler 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This work was supported by a SNSF PRIMA  grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We are grateful to LMSAL for allowing us to download the IRIS database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  IRIS is a NASA small explorer mission developed and operated by LMSAL with  mission operations executed at NASA Ames Research Center and major contri-  butions to downlink communications funded by ESA and the Norwegian Space  Centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='  An input spectrum x is fed into the network which stimulates the hid-  den layer causing the neurons (black circles) to produce output signals  that are proportional to the weighted linear sum of the spectrum’s in-  tensities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The content of each neuron is then passed through a nonlinear  activation function g, such as a softmax or ReLU, which allows the net-  work to approximate a large set of complex behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content=' The neuron which produces the strongest signal represents  the network’s prediction on whether the spectrum comes from the AR  or PF class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The weight matrices Θ1,2 determine how information flows  through the network and are updated by propagating the errors from a  set of predictions back through the network, and adjusting the individual  weights against a loss function via gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  the fact that every neuron has a connection to every other neuron  in the layers surrounding it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each neuron is therefore in commu-  nication with all the neurons from the preceding layer, and the  strength of the signal between any two neurons is modulated by  the models weights {θ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The connections between each layer are  therefore summarized by two matrices Θ1 and Θ2, where each  entry θij from one of these matrices corresponds to the ease of  communication between two inter-layer neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The term "feed forward" refers to the fact that information  flows forward through the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The magnitude of the re-  sponse in neuron j is simply a weighted linear sum of the inputs  according to their weights z = �  i θijxi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This sum is then passed  through a function g(z), referred to as an activation function,  which is necessarily nonlinear and allows the network to approx-  imate a large set of complex functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In our case, the content of  the collective stimulation in each of our neurons passes through a  ReLU activation function g(z j) = z+  j = max(0, z j) except for the  final output layer, which produces a probability by passing the  signal through a softmax function g(z j) = exp(zj)/ �  i exp(zi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The two final neurons vote for either the AR or PF class, and  the neuron that has the strongest signal represents the network’s  prediction ˆyc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The randomly initiated weights of the network are optimized  by minimizing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Although prediction is performed by al-  lowing information to flow forward through the network, opti-  mization is performed by propagating the collective errors from  the prediction back through the network using an algorithm re-  ferred to as backpropagation, a NN equivalent to gradient de-  scent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The network therefore combs through 64 spectra pro-  ducing a prediction for each instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The loss is then calcu-  lated using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1, and the network’s weights are updated using  backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This procedure is continued for several epochs  (passes over the entire dataset), adjusting the weights and flow  of information through the network, so that some signals are  strengthened while others attenuated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Appendix B: Grad-CAM (detailed description)  We know that each feature map is activated by some visual pat-  tern within the input, such as triplet emission or broad line cores,  and furthermore that feature maps in deeper layers are capa-  ble of extracting more sophisticated representations of the input  (Zeiler & Fergus 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An important observation when look-  ing at Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 5, is to note that the original input spectrum can be  roughly reconstructed by placing each of the final feature map  activations on-top of one another (summing them together).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To  makes this clear, feature map A1 identifies the triplet emission,  A2 the h-core, A3 the pseudo continuum, and A4 the k-core, thus  superimposing all the maps leads to a reconstruction of the orig-  inal spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Grad-CAM is used to identify which of the four  final maps are most important for the classification task, which  for our problem translates to which features of each spectrum  are strongly related to preflares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' After ranking the maps in order  of importance, each map can then be assigned a weight before  they are summed together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Because each map is weighted differ-  ently, the sum of the maps now no longer reproduce the original  spectrum, but rather a vector of values whose magnitude at each  index represents that pixel’s/wavelength’s importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This vec-  tor in other words is our heatmap that can be projected back onto  the original spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The question now is how does Grad-CAM assign weights to  each map?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The mechanism for doing this is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Grad-CAM looks at the maps in the final convolutional layer  (dashed box in the figure), and assigns weights to each map by  monitoring how sensitive (to first order) the resultant output pre-  diction yc is to small variations of the map Ak  i , where the index  i runs over the individual pixels of the map and c represents the  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The weight αc  k assigned to each map is simply the average  (global pooling) of the gradients within each pixel of the map  αc  k = 1  Z  �  i  ∂yc  ∂Ak  i  ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1)  where in our case Z = 22, the number of pixels in an individual  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The saliency map is therefore given by  Mc = ReLU  �������  �  k  αc  kAk  ������� ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2)  where the role of the ReLU function is to suppress the contri-  butions from the negative (AR) class, thus producing a saliency  map that only highlights the features deemed important for the  classification of PF spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' As seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2, the resulting  coarse heatmap Mc has to first be interpolated to the size of the  input spectrum (240 pixels) before it can be projected onto the  input and interpreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  There are several nuances that we list here to clear any con-  fusion about the results produced by Grad-CAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1) Although  the filters/kernels are fixed in a trained model, different spectra  can lead to different activations and therefore different feature  maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This property is referred to as locality, meaning that Grad-  CAM produces only local explanations specific to each example  spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2) A single feature map need not find patterns that are  spatially connected in the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For instance, if a kernel learned  weights that lead to activations and a feature map that identifies  Article number, page 17 of 21  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  global pool  CAM  last convolutional layer  (240)  (2, 74)  (4, 22)  (4, 11)  (44)  (5)  (2)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Schematic of Grad-CAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A single spectrum x is passed into a ConvNet that has been trained to distinguish between the PF/AR datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The last convolutional layer before the max pooling and fully connected layers contains the network’s most sophisticated understanding of the  spectrum, with each of the four feature maps Ak, focusing on different aspects deemed important for the classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The average gradients  αc  k of the output prediction are taken with respect to each of the maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Larger gradients indicate that the features identified by a particular map are  more important for the classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' All four feature maps are then scaled by their corresponding importance and summed before being passed  through a ReLU function that isolates the features the network focuses on for the positive classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The resultant CAM heat map is then  interpolated from the scale of the feature map to the dimensionality of the input data before being projected onto the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  noise, then assuming that the cores have the best signal-to-noise,  the maps would disjointly activate over the continuum left and  right of both cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 3) Due to the successive use of convolutions,  the feature maps shrink in width as the information flows deeper  into the network, meaning that the derived saliency map is often  much smaller in size than the input spectrum and has to be inter-  polated back to the original size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Therefore, network architecture  dictates the resolution of the final heatmap, with extremely deep  networks having poor heatmap resolution, and extremely shal-  low networks lacking sophisticated explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This last point  highlights a weakness of Grad-CAM, namely that the success of  quality explanations depends strongly on the selection criterion  of the network’s architecture, which in itself is done via trial and  error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Our solution to this final point was to construct several net-  work architectures with different depths, number of convolu-  tions, as well as differing structures of the fully connected lay-  ers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We found that the problem was simple enough to address  with the relatively minimalistic architecture shown in Fig A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2,  and that going deeper resulted in poor resolution, while a single  convolutional layer produced poor quality explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An ul-  timate confirmation of our architectural choice however is best  supported by using an alternative method that does not itself de-  pend strongly on the specific architecture of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Appendix C: EG (detailed description)  EG utilizes the idea of "missingness" which is a common con-  cept in cooperative game theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The idea is that if we remove  wavelengths from the input spectrum, then those missing wave-  lengths that affect the prediction of the network most must be  more critical for its discrimination task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In order to weigh wave-  length importance via this method requires one to average over  all possible subsets (or coalitions) of wavelengths to ensure the  fair distribution of importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The need for subsetting becomes clear if one considers the  very likely scenario where two neighboring wavelengths contain  the same information, and furthermore, that this information is  responsible for 90% of the network’s decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' By simply re-  moving one wavelength at a time, the performance of the net-  work will never drop significantly, since the partner wavelength  will always carry the discriminant load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Counter-intuitively, this  might result in the two most important wavelengths being ranked  as useless, which is not such an unlikely scenario if one consid-  ers that proximal wavelengths in a high-resolution spectrogram  such as IRIS are likely to transmit similar types of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  A complete formalism that allows for the fair distribution of  wavelength relevance can be found in the game theoretic quan-  tity called the Shapley value (Shapley 1951), given by  φλ(FΘ) =  �  S ⊂N  (s − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' (n − s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  [FΘ(S ) − FΘ(S − λ)],  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1)  where |N| = n = 240 is the total number of λ-points, |S | = s is a  subset of those wavelengths, λ represents a single input wave-  length, whose importance we are trying to calculate, and FΘ  is the characteristic function giving us the subset’s "worth".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If  we parameterize the characteristic function FΘ with a ConvNet  trained on the binary classification PF/AR problem, then we can  interpret the Shapley value for a particular wavelength λ and in-  put spectrum x, as the expected difference between the predic-  tion ˆy over all lambda coalitions/subsets, with and without said  wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The prefactor (s − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' (n − s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='/n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' weights each score discrep-  ancy by the number of ways a particular subset of pixels can  be formed (in our case each of the n-wavelengths are equally  likely), and allows us to alternatively interpret the Shapley value  Article number, page 18 of 21  Brandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  φλ as the expected marginal contribution of λ to the network’s  output prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  The question now is how to reformulate Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1 so that it is  compatible with functions FΘ that are parameterized by NNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' An  important caveat is that NNs have fixed architectures, so one can-  not simply remove input channels when subsetting over wave-  length coalitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This means that NNs require each wavelength  to pump information through it at all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' A solution is there-  fore to construct a baseline that represents missingness and can  be fed through the network constantly without affecting the re-  sults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this way, we can artificially turn some wavelengths off  while still respecting the constant flow of information through  the networks input channels, allowing us to form pseudo subsets  to approximate the form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  This baseline must be selected with great care, since it can  severely affect and bias the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For instance, if one assumes  that missingness is best represented by zeros, then the black re-  gions of any image (such as outline contours) or low intensity  portions of any spectrum (which might be the most critical as-  pects) would be considered useless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Another common choice of  baseline is to inject Gaussian noise into some wavelengths so  that with many forward passes through the network, the average  contribution of said wavelength becomes negligible (Smilkov  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This baseline however ignores the very real fact  that neighboring, as well as disjoint wavelengths might be cor-  related to one another, and not independently distributed as such  distributions would assume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Arguably, the correct baseline, and the strategy employed  by EG, is to represent missingness by the actual dataset itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Like the Gaussian distribution, flooding combinations/subsets of  wavelengths with the intensities found within the dataset, would  result in a zero net average displacement of the network’s pre-  diction score for a particular spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' To see why, consider that  after randomly sampling particular combinations of intensities  from the dataset, it is likely that some features emerge from the  AR class, leading to a decrease in the network’s output predic-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' At the same time, the sampling is equally likely to counter-  balance this shift by allowing particular features associated with  the PF class to emerge, resulting in an increase to the score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In  addition to the invariant behaviour of the score under this type  of sampling (a fact that is critical for the formation of pseudo  subsets), it also respects the full set of correlations and inter-  dependencies that exist between the wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Figure C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1 demonstrates how EG derives the heatmap for a  particular PF spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Each of the rows in the figure represent  a path in image space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In each case, we start from some base-  line for missingness, that is, a specific spectrum from the con-  joined PF/AR dataset (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In each row, EG interpolates from  left to right between the baseline spectrum and a particular tar-  get spectrum (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Notice that although the baseline starts  from different points in the image space, that is, different spec-  tra, the target is always the same spectrum for which we want  to calculate the heatmap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' As we vary α from 0 to 1, the features  of the target spectrum (such as triplet emission) slowly emerge  from the baseline and become dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' At each point along a  particular path, we feed the interpolated spectra into the network  FΘ and calculate its prediction score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We can then estimate which wavelengths contributed most  to the output score by calculating the difference between scores  of successive images along a path and monitoring the accumu-  lated gradient of the output with respect to each wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Those wavelengths that are critical for the network’s decision  will affect the output’s prediction most.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For instance, in the case  Same target spectrum  Trained  ConvNet  EG heatmap  Different baselines  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Diagram showing the calculation procedure for producing an  EG heatmap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The heatmap for a target spectrum (orange) is calculated  by interpolating between a set of baseline spectra (blue) and the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  As we move from left to right along each row, the interpolated spec-  trum in each panel is fed into the network which generates a prediction  score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The wavelengths with the largest accumulated gradients along  the path are then ranked as most critical for flare prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Instead of  integrating over all paths, EG calculates an expectation value for the  wavelength’s importance by feeding a random sample (gray spectra)  into the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  shown here, the triplet emission is not present at the start of the  path, but slowly emerges as we get closer to the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' If the  network thinks this feature is important, the output will depend  most strongly on these wavelengths and accumulate the steepest  gradients as we travel along the image path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  We therefore understand that integrating along α while mon-  itoring the accumulated gradients along a single path is analo-  gous to calculating the difference between scores under a single  subset, reproducing the functionality of [FΘ(S ) − FΘ(S − λ)]  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' However this subset at the moment is "dirty", since  we have a single baseline from the dataset whose effects only  become negligible when averaged over many paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In order to  unbiase our baseline, as well as form pseudo subsets over ev-  ery combination of wavelengths, we need to gain an additional  integration term over x′ and integrate over all image paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Putting this all together, a mathematically concise NN equiv-  alent of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1 is given by  φλ|EG =  �  x′  ��xλ − x′  λ  � ×  ×  � 1  α=0  δFΘ (x′ + α (x − x′))  δxλ  dα  �  pD  �x′� dx′  ≃  E  x′∼D,α∼U(0,1)  ��xλ − x′  λ  � δFΘ (x′ + α × (x − x′))  δxλ  �  ,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2)  where the first integral over x′ selects the baseline starting point,  and at heart is responsible for generating our pseudo subsets over  wavelength allegiances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The second integral over α propagates  us along a particular path as defined by x′, such that the target  spectrum (orange) emerges from the baseline as α|0 → 1, al-  lowing us to calculate the differences between scores with and  without particular features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The function FΘ as usual represents  our ConvNet, which is the same as that used for Grad-CAM,  and was trained on the binary PF/AR classification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Fi-  nally D means that our baseline samples form the actual dataset,  which as discussed above results in a net zero effect on the output  score when averaged over many samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Crucially, this choice  of baseline also respect the existence of a rich set of correlations  that exist between different wavelengths, something a Gaussian  analog for missingness would neglect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Article number, page 19 of 21  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' XAI  Since the process of integrating over all complete image  paths is computationally infeasible, EG takes the expectation  value along a set of randomly selected paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1 this  is represented by only feeding the NN the spectra from the ran-  domly selected gray highlighted panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' It has been shown that  the expectation converges and that the results respect several  important interpretability axioms such as completeness, where  each wavelength’s attributions sums to the network’s output pre-  diction (Gabriel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' For our purposes we found that a  baseline sample of 500 spectra was sufficient for EG to converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Normally the heatmaps derived from such path attribution  methods do not necessarily produce smooth outputs, that is, attri-  butions between neighboring wavelengths can be large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In many  cases one would assume that neighboring wavelengths would re-  lay similar types of information and therefore produce smooth  attributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Much work has gone into encouraging such intuitive  restrictions over the derived explanations (Rieger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  For EG, this is normally achieved by incorporating the attribu-  tions into a prior, and wrapping them into a differentiable func-  tion that promotes smooth attributions across neighboring wave-  lengths, while penalizing heatmaps with large amounts of local  variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this way, the attributions form part of the training  procedure, and on some datasets actually improve model perfor-  mance and convergence time (Gabriel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We attempted  to incorporate this prescription by defining the generalized loss  function  S(Θ, x) = L(Θ, X)  ����������  BCE  + σ  �  x,λ  |φ(x)λ+1 − φ(x)λ|  ��������������������������������������������������  attribution prior  ,  (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3)  with the first term L being the standard binary cross-entropy  as discussed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 1, and the second term a differentiable at-  tribution prior consisting of wavelength attributions φ(x)λ from  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' This term promotes the variations between attributions  of neighboring wavelengths to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Here, σ is a regulariza-  tion parameter that controls the trade-off between smooth attri-  butions and model accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Unfortunately, following this prescription did not result in  smooth heatmaps for the case of our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The smoothing effect  only initiated after the classification score became small, which  tended to always be after the point where the model overfitted the  training data, resulting in a divergent validation loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' When we  tried to increase the hyperparameter σ such that the smoothing  would initiate before the critical overfitting point, the network’s  classification score suffered and rapidly diverged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' We therefore  selected to add a manual small smoothing post-hoc (after train-  ing) for increased interpretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' The degree of smoothing was  adjusted until the heatmaps matched those derived from grad-  CAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  As a point of analogy, grad-CAM naturally smooths its at-  tributions due to the coarse feature maps that result from the di-  mensionality bottleneck brought about by consecutive convolu-  tional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' In this case attributions are assigned on an 22-point  grid (final feature map dimension) and then upscaled to the res-  olution of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' EG on the other hand always operates and  derives its attributions at the resolution of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Appendix D: Supplementary figures  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14, but for nonflare (AR) events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' 14, but an example of how the location of the  maximum attributions along the slit in the preflare region (bottom panel,  left) align with the maximum UV emission of the flare (upper panel,  right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' Notice that even though the intensity is larger around pixel 160,  the attributions are only high around pixels 130, where the maximum  UV intensity is seen later during the flare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='  Article number, page 20 of 21  Observation:201510170031153660105403,SlitPosition:0  350  300  X  250  Intensity  e  200  M  P  150  100  50  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='20  350  Expected Gradients  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='19  300  tance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='18  250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='17  e  200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='16  150  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='15  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='14  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='13  0  0  50  100  150  200  250  300  350  400  450  IRIS rasterObservation:20150809061551  3860009180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='SlitPosition:0  700  X  600  500  Intensity  400  M  P  300  200  C  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='30  700  Expected Gradients  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='28  600  ortance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='52  150  ortance  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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+page_content='32  0  360  368  376  384  392  400  408  416  424  432  440  448  456  464  472  IRIS rasterBrandon Panos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' : Identifying preflare spectral features using explainable artificial intelligence  Table A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content=' PF observations  #  Class  Date and time  Observation mode  CAD  FOV center  OBSID  when raster started  (sec)  (arcsec)  1  M6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='5  2015-06-22T17:00  Large sparse 16-step raster  33  (72,192)  3660100039  2  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2014-11-07T09:37  Large coarse 16-step raster  23  (-646,224)  3860602088  3  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1  2015-08-21T16:01  Medium dense 32-step raster  102  (-467,-336)  3660104044  4  M3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='9  2014-06-11T18:19  Medium coarse 8-step raster  21  (-781,-306)  3863605329  5  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  2015-03-11T04:46  Large coarse 8-step raster  75  (-430,-194)  3860259280  6  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1  2014-09-06T11:23  Large sit-and-stare  9  (-709,-298)  3820259253  7  M3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  2014-10-27T20:56  Large sit-and-stare  16  (779,-271)  3864111353  8  X2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='1  2015-03-11T15:19  Large coarse 4-step raster  16  (-353,-197)  3860107071  9  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2014-06-12T18:44  Medium coarse 8-step raster  21  (-670,-306)  3863605329  10  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='8  2014-02-12T21:50  Large coarse 8-step raster  42  (140,-90)  3860257280  11  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3  2014-10-26T18:52  Large sit-and-stare  16  (648,-287)  3864111353  12  X2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2014-10-27T14:04  Large coarse 8-step raster  26  (727,-299)  3860354980  13  M2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='3  2014-11-09T15:17  Large coarse 4-step raster  37  (-217,-205)  3860258971  14  X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2014-03-29T14:09  Very large coarse 8-step raster  72  (490,282)  3860258481  15  X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6  2014-10-22T08:18  Very large coarse 8-step raster  131  (-292,-303)  3860261381  16  M1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='4  2015-03-12T05:45  Large sit-and-stare  5  (-185,-190)  3860107053  17  X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='0  2014-10-25T14:58  Large sit-and-stare  5  (408,-319)  3880106953  18  X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='6  2014-09-10T11:28  Large sit-and-stare  9  (-137,125)  3860259453  19  M8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='7  2014-10-21T18:10  Large sit-and-stare  16  (-359,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-316)  3860261353  AR-observations  1  2015-05-18T14:39  Large coarse 4-step raster  21  (300,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-98)  3860256971  2  2015-05-18T16:14  Large coarse 4-step raster  21  (315,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-95)  3860256971  3  2015-05-21T18:59  Very large sit-and-stare  5  (-382,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='398)  3800507454  4  2015-07-03T16:59  Large sparse 8-step raster  45  (-186,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='213)  3620006130  5  2015-07-04T10:09  Very large sit-and-stare  9  (86,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='174)  3860108354  6  2015-07-04T16:59  Large sparse 8-step raster  44  (20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='202)  3620006130  7  2015-07-28T15:18  Medium coarse 4-step raster  37  (-227,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-289)  3660109122  8  2015-08-07T22:14  Large coarse 8-step raster  74  (547,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='125)  3860259180  9  2015-08-09T06:15  Large coarse 8-step raster  75  (-236,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-370)  3860009180  10  2015-09-16T18:17  Medium coarse 16-step raster  34  (-564,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-356)  3600101141  11  2015-10-17T00:31  Large sit-and-stare  3  (-558,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-233)  3660105403  12  2015-07-24T05:35  Large sit-and-stare  9  (557,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
+page_content='-204)  3620109103  13  2015-04-08T04:57  Large sit-and-stare  5  (45,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/WdAzT4oBgHgl3EQfmP2O/content/2301.01560v1.pdf'}
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