Daily Papers

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.

In causal inference, estimating heterogeneous treatment effects (HTE) is critical for identifying how different subgroups respond to interventions, with broad applications in fields such as precision medicine and personalized advertising. Although HTE estimation methods aim to improve accuracy, how to provide explicit subgroup descriptions remains unclear, hindering data interpretation and strategic intervention management. In this paper, we propose CURLS, a novel rule learning method leveraging HTE, which can effectively describe subgroups with significant treatment effects. Specifically, we frame causal rule learning as a discrete optimization problem, finely balancing treatment effect with variance and considering the rule interpretability. We design an iterative procedure based on the minorize-maximization algorithm and solve a submodular lower bound as an approximation for the original. Quantitative experiments and qualitative case studies verify that compared with state-of-the-art methods, CURLS can find subgroups where the estimated and true effects are 16.1% and 13.8% higher and the variance is 12.0% smaller, while maintaining similar or better estimation accuracy and rule interpretability. Code is available at https://osf.io/zwp2k/.

Despite excellent average-case performance of many image classifiers, their performance can substantially deteriorate on semantically coherent subgroups of the data that were under-represented in the training data. These systematic errors can impact both fairness for demographic minority groups as well as robustness and safety under domain shift. A major challenge is to identify such subgroups with subpar performance when the subgroups are not annotated and their occurrence is very rare. We leverage recent advances in text-to-image models and search in the space of textual descriptions of subgroups ("prompts") for subgroups where the target model has low performance on the prompt-conditioned synthesized data. To tackle the exponentially growing number of subgroups, we employ combinatorial testing. We denote this procedure as PromptAttack as it can be interpreted as an adversarial attack in a prompt space. We study subgroup coverage and identifiability with PromptAttack in a controlled setting and find that it identifies systematic errors with high accuracy. Thereupon, we apply PromptAttack to ImageNet classifiers and identify novel systematic errors on rare subgroups.

Let E be the HNN-extension of a group B with subgroups H and K associated according to an isomorphism varphicolon H to K. Suppose that H and K are normal in B and (H cap K)varphi = H cap K. Under these assumptions, we prove necessary and sufficient conditions for E to be residually a C-group, where C is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual p-finiteness of the group E.

We present the Mixture-of-Tunable-Experts (MoTE), a method that extends the Mixture-of-Experts architecture of Large Language Models (LLMs). Without additional training, MoTE enables meaningful and focused behavior changes in LLMs on-the-fly during inference time. By analyzing the digital LLM brain of DeepSeek-R1 using a technique we dub 'functional Token Resonance Imaging' (fTRI) -- inspired by fMRI and using prompts designed to elicit specific behavior (e.g., 'What happened {time}{place}?') -- we empirically identify distinctive experts associated with behaviors like refusal responses. Using MoTE we are able to intervene and control such specific behavior. We switched off the top 10 most refusal-relevant experts (0.07% of R1's 14,848 routed experts), achieving a 52% refusal reduction on sensitive reference prompts without performance degradation on MT-Bench. Random expert deactivation resulted in smaller behavioral shifts with increased noise, whereas forced expert activation led to significantly higher refusal rates. Our approach shares similarities with sparse autoencoders (SAEs) in terms of explainability and steerability. Unlike SAEs, MoTE does not require large training efforts, as within MoEs with a vast number of experts, specialization already emerged naturally during pretraining. Our findings suggest that significant functional mechanisms in Mixture-of-Experts architectures can at least partially be localized in a small number of specific experts, rather than being distributed throughout the model's weights. Expert subgroups can be tuned to trigger significant behavior variations, providing insights into the inner workings of LLMs.

The advancement of large language models (LLMs) has made it difficult to differentiate human-written text from AI-generated text. Several AI-text detectors have been developed in response, which typically utilize a fixed global threshold (e.g., {\theta} = 0.5) to classify machine-generated text. However, we find that one universal threshold can fail to account for subgroup-specific distributional variations. For example, when using a fixed threshold, detectors make more false positive errors on shorter human-written text than longer, and more positive classifications on neurotic writing styles than open among long text. These discrepancies can lead to misclassification that disproportionately affects certain groups. We address this critical limitation by introducing FairOPT, an algorithm for group-specific threshold optimization in AI-generated content classifiers. Our approach partitions data into subgroups based on attributes (e.g., text length and writing style) and learns decision thresholds for each group, which enables careful balancing of performance and fairness metrics within each subgroup. In experiments with four AI text classifiers on three datasets, FairOPT enhances overall F1 score and decreases balanced error rate (BER) discrepancy across subgroups. Our framework paves the way for more robust and fair classification criteria in AI-generated output detection.

Recent work in vision-and-language demonstrates that large-scale pretraining can learn generalizable models that are efficiently transferable to downstream tasks. While this may improve dataset-scale aggregate metrics, analyzing performance around hand-crafted subgroups targeting specific bias dimensions reveals systemic undesirable behaviors. However, this subgroup analysis is frequently stalled by annotation efforts, which require extensive time and resources to collect the necessary data. Prior art attempts to automatically discover subgroups to circumvent these constraints but typically leverages model behavior on existing task-specific annotations and rapidly degrades on more complex inputs beyond "tabular" data, none of which study vision-and-language models. This paper presents VLSlice, an interactive system enabling user-guided discovery of coherent representation-level subgroups with consistent visiolinguistic behavior, denoted as vision-and-language slices, from unlabeled image sets. We show that VLSlice enables users to quickly generate diverse high-coherency slices in a user study (n=22) and release the tool publicly.

Machine learning models often perform poorly on subgroups that are underrepresented in the training data. Yet, little is understood on the variation in mechanisms that cause subpopulation shifts, and how algorithms generalize across such diverse shifts at scale. In this work, we provide a fine-grained analysis of subpopulation shift. We first propose a unified framework that dissects and explains common shifts in subgroups. We then establish a comprehensive benchmark of 20 state-of-the-art algorithms evaluated on 12 real-world datasets in vision, language, and healthcare domains. With results obtained from training over 10,000 models, we reveal intriguing observations for future progress in this space. First, existing algorithms only improve subgroup robustness over certain types of shifts but not others. Moreover, while current algorithms rely on group-annotated validation data for model selection, we find that a simple selection criterion based on worst-class accuracy is surprisingly effective even without any group information. Finally, unlike existing works that solely aim to improve worst-group accuracy (WGA), we demonstrate the fundamental tradeoff between WGA and other important metrics, highlighting the need to carefully choose testing metrics. Code and data are available at: https://github.com/YyzHarry/SubpopBench.

Vision-language models (VLMs) are highly effective but often underperform on specialized tasks; for example, Llava-1.5 struggles with chart and diagram understanding due to scarce task-specific training data. Existing training data, sourced from general-purpose datasets, fails to capture the nuanced details needed for these tasks. We introduce MM-Gen, a scalable method that generates task-specific, high-quality synthetic text for candidate images by leveraging stronger models. MM-Gen employs a three-stage targeted process: partitioning data into subgroups, generating targeted text based on task descriptions, and filtering out redundant and outlier data. Fine-tuning VLMs with data generated by MM-Gen leads to significant performance gains, including 29% on spatial reasoning and 15% on diagram understanding for Llava-1.5 (7B). Compared to human-curated caption data, MM-Gen achieves up to 1.6x better improvements for the original models, proving its effectiveness in enhancing task-specific VLM performance and bridging the gap between general-purpose datasets and specialized requirements. Code available at https://github.com/sjoshi804/MM-Gen.

Transformers and large language models~(LLMs) have seen rapid adoption in all domains. Their sizes have exploded to hundreds of billions of parameters and keep increasing. Under these circumstances, the training of transformers is very expensive and often hits a ``memory wall'', i.e., even when using 3D parallelism (pipeline, tensor, data) and aggregating the memory of many GPUs, it is still not enough to hold the necessary data structures (model parameters, optimizer state, gradients, activations) in GPU memory. To compensate, state-of-the-art approaches offload the optimizer state, at least partially, to the host memory and perform hybrid CPU-GPU computations. However, the management of the combined host-GPU memory is often suboptimal and results in poor overlapping between data movements and computations. This leads to missed opportunities to simultaneously leverage the interconnect bandwidth and computational capabilities of CPUs and GPUs. In this paper, we leverage a key observation that the interleaving of the forward, backward and update phases generate fluctuations in the GPU memory utilization, which can be exploited to dynamically move a part of the optimizer state between the host and the GPU memory at each iteration. To this end, we design and implement \proj, a novel technique to split the LLM into subgroups, whose update phase is scheduled on either the CPU or the GPU based on our proposed performance model that addresses the trade-off between data movement cost, acceleration on the GPUs vs the CPUs, and competition for shared resources. We integrate our approach with DeepSpeed and demonstrate 2.5times faster iterations over state-of-the-art approaches using extensive experiments.

Speech models may be affected by performance imbalance in different population subgroups, raising concerns about fair treatment across these groups. Prior attempts to mitigate unfairness either focus on user-defined subgroups, potentially overlooking other affected subgroups, or do not explicitly improve the internal representation at the subgroup level. This paper proposes the first adoption of contrastive learning to mitigate speech model bias in underperforming subgroups. We employ a three-level learning technique that guides the model in focusing on different scopes for the contrastive loss, i.e., task, subgroup, and the errors within subgroups. The experiments on two spoken language understanding datasets and two languages demonstrate that our approach improves internal subgroup representations, thus reducing model bias and enhancing performance.

Despite the proven effectiveness of Transformer neural networks across multiple domains, their performance with Electronic Health Records (EHR) can be nuanced. The unique, multidimensional sequential nature of EHR data can sometimes make even simple linear models with carefully engineered features more competitive. Thus, the advantages of Transformers, such as efficient transfer learning and improved scalability are not always fully exploited in EHR applications. Addressing these challenges, we introduce SANSformer, an attention-free sequential model designed with specific inductive biases to cater for the unique characteristics of EHR data. In this work, we aim to forecast the demand for healthcare services, by predicting the number of patient visits to healthcare facilities. The challenge amplifies when dealing with divergent patient subgroups, like those with rare diseases, which are characterized by unique health trajectories and are typically smaller in size. To address this, we employ a self-supervised pretraining strategy, Generative Summary Pretraining (GSP), which predicts future summary statistics based on past health records of a patient. Our models are pretrained on a health registry of nearly one million patients, then fine-tuned for specific subgroup prediction tasks, showcasing the potential to handle the multifaceted nature of EHR data. In evaluation, SANSformer consistently surpasses robust EHR baselines, with our GSP pretraining method notably amplifying model performance, particularly within smaller patient subgroups. Our results illuminate the promising potential of tailored attention-free models and self-supervised pretraining in refining healthcare utilization predictions across various patient demographics.

Commonsense knowledge (CSK) about concepts and their properties is useful for AI applications such as robust chatbots. Prior works like ConceptNet, TupleKB and others compiled large CSK collections, but are restricted in their expressiveness to subject-predicate-object (SPO) triples with simple concepts for S and monolithic strings for P and O. Also, these projects have either prioritized precision or recall, but hardly reconcile these complementary goals. This paper presents a methodology, called Ascent, to automatically build a large-scale knowledge base (KB) of CSK assertions, with advanced expressiveness and both better precision and recall than prior works. Ascent goes beyond triples by capturing composite concepts with subgroups and aspects, and by refining assertions with semantic facets. The latter are important to express temporal and spatial validity of assertions and further qualifiers. Ascent combines open information extraction with judicious cleaning using language models. Intrinsic evaluation shows the superior size and quality of the Ascent KB, and an extrinsic evaluation for QA-support tasks underlines the benefits of Ascent. A web interface, data and code can be found at https://ascent.mpi-inf.mpg.de/.

In critical decision-making scenarios, optimizing accuracy can lead to a biased classifier, hence past work recommends enforcing group-based fairness metrics in addition to maximizing accuracy. However, doing so exposes the classifier to another kind of bias called infra-marginality. This refers to individual-level bias where some individuals/subgroups can be worse off than under simply optimizing for accuracy. For instance, a classifier implementing race-based parity may significantly disadvantage women of the advantaged race. To quantify this bias, we propose a general notion of eta-infra-marginality that can be used to evaluate the extent of this bias. We prove theoretically that, unlike other fairness metrics, infra-marginality does not have a trade-off with accuracy: high accuracy directly leads to low infra-marginality. This observation is confirmed through empirical analysis on multiple simulated and real-world datasets. Further, we find that maximizing group fairness often increases infra-marginality, suggesting the consideration of both group-level fairness and individual-level infra-marginality. However, measuring infra-marginality requires knowledge of the true distribution of individual-level outcomes correctly and explicitly. We propose a practical method to measure infra-marginality, and a simple algorithm to maximize group-wise accuracy and avoid infra-marginality.

A membership inference attack (MIA) against a machine-learning model enables an attacker to determine whether a given data record was part of the model's training data or not. In this paper, we provide an in-depth study of the phenomenon of disparate vulnerability against MIAs: unequal success rate of MIAs against different population subgroups. We first establish necessary and sufficient conditions for MIAs to be prevented, both on average and for population subgroups, using a notion of distributional generalization. Second, we derive connections of disparate vulnerability to algorithmic fairness and to differential privacy. We show that fairness can only prevent disparate vulnerability against limited classes of adversaries. Differential privacy bounds disparate vulnerability but can significantly reduce the accuracy of the model. We show that estimating disparate vulnerability to MIAs by na\"ively applying existing attacks can lead to overestimation. We then establish which attacks are suitable for estimating disparate vulnerability, and provide a statistical framework for doing so reliably. We conduct experiments on synthetic and real-world data finding statistically significant evidence of disparate vulnerability in realistic settings. The code is available at https://github.com/spring-epfl/disparate-vulnerability

Large Language Models (LLMs) are thought to struggle with arithmetic learning due to the inherent differences between language modeling and numerical computation, but concrete evidence has been lacking. This work responds to this claim through a two-side experiment. We first investigate whether LLMs leverage partial products during arithmetic learning. We find that although LLMs can identify some partial products after learning, they fail to leverage them for arithmetic tasks, conversely. We then explore how LLMs approach arithmetic symbolically by breaking tasks into subgroups, hypothesizing that difficulties arise from subgroup complexity and selection. Our results show that when subgroup complexity is fixed, LLMs treat a collection of different arithmetic operations similarly. By analyzing position-level accuracy across different training sizes, we further observe that it follows a U-shaped pattern: LLMs quickly learn the easiest patterns at the first and last positions, while progressively learning the more difficult patterns in the middle positions. This suggests that LLMs select subgroup following an easy-to-hard paradigm during learning. Our work confirms that LLMs are pure symbolic learners in arithmetic tasks and underscores the importance of understanding them deeply through subgroup-level quantification.

The proliferation of machine learning models in critical decision making processes has underscored the need for bias discovery and mitigation strategies. Identifying the reasons behind a biased system is not straightforward, since in many occasions they are associated with hidden spurious correlations which are not easy to spot. Standard approaches rely on bias audits performed by analyzing model performance in pre-defined subgroups of data samples, usually characterized by common attributes like gender or ethnicity when it comes to people, or other specific attributes defining semantically coherent groups of images. However, it is not always possible to know a-priori the specific attributes defining the failure modes of visual recognition systems. Recent approaches propose to discover these groups by leveraging large vision language models, which enable the extraction of cross-modal embeddings and the generation of textual descriptions to characterize the subgroups where a certain model is underperforming. In this work, we argue that incorporating visual explanations (e.g. heatmaps generated via GradCAM or other approaches) can boost the performance of such bias discovery and mitigation frameworks. To this end, we introduce Visually Grounded Bias Discovery and Mitigation (ViG-Bias), a simple yet effective technique which can be integrated to a variety of existing frameworks to improve both, discovery and mitigation performance. Our comprehensive evaluation shows that incorporating visual explanations enhances existing techniques like DOMINO, FACTS and Bias-to-Text, across several challenging datasets, including CelebA, Waterbirds, and NICO++.

Fair machine learning seeks to mitigate model prediction bias against certain demographic subgroups such as elder and female. Recently, fair representation learning (FRL) trained by deep neural networks has demonstrated superior performance, whereby representations containing no demographic information are inferred from the data and then used as the input to classification or other downstream tasks. Despite the development of FRL methods, their vulnerability under data poisoning attack, a popular protocol to benchmark model robustness under adversarial scenarios, is under-explored. Data poisoning attacks have been developed for classical fair machine learning methods which incorporate fairness constraints into shallow-model classifiers. Nonetheless, these attacks fall short in FRL due to notably different fairness goals and model architectures. This work proposes the first data poisoning framework attacking FRL. We induce the model to output unfair representations that contain as much demographic information as possible by injecting carefully crafted poisoning samples into the training data. This attack entails a prohibitive bilevel optimization, wherefore an effective approximated solution is proposed. A theoretical analysis on the needed number of poisoning samples is derived and sheds light on defending against the attack. Experiments on benchmark fairness datasets and state-of-the-art fair representation learning models demonstrate the superiority of our attack.

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

Differential privacy (DP) is a popular mechanism for training machine learning models with bounded leakage about the presence of specific points in the training data. The cost of differential privacy is a reduction in the model's accuracy. We demonstrate that in the neural networks trained using differentially private stochastic gradient descent (DP-SGD), this cost is not borne equally: accuracy of DP models drops much more for the underrepresented classes and subgroups. For example, a gender classification model trained using DP-SGD exhibits much lower accuracy for black faces than for white faces. Critically, this gap is bigger in the DP model than in the non-DP model, i.e., if the original model is unfair, the unfairness becomes worse once DP is applied. We demonstrate this effect for a variety of tasks and models, including sentiment analysis of text and image classification. We then explain why DP training mechanisms such as gradient clipping and noise addition have disproportionate effect on the underrepresented and more complex subgroups, resulting in a disparate reduction of model accuracy.

Since late 2022, Large Language Models (LLMs) have become very prominent with LLMs like ChatGPT and Bard receiving millions of users. Hundreds of new LLMs are announced each week, many of which are deposited to Hugging Face, a repository of machine learning models and datasets. To date, nearly 16,000 Text Generation models have been uploaded to the site. Given the huge influx of LLMs, it is of interest to know which LLM backbones, settings, training methods, and families are popular or trending. However, there is no comprehensive index of LLMs available. We take advantage of the relatively systematic nomenclature of Hugging Face LLMs to perform hierarchical clustering and identify communities amongst LLMs using n-grams and term frequency-inverse document frequency. Our methods successfully identify families of LLMs and accurately cluster LLMs into meaningful subgroups. We present a public web application to navigate and explore Constellation, our atlas of 15,821 LLMs. Constellation rapidly generates a variety of visualizations, namely dendrograms, graphs, word clouds, and scatter plots. Constellation is available at the following link: https://constellation.sites.stanford.edu/.

Intersectionality is a critical framework that, through inquiry and praxis, allows us to examine how social inequalities persist through domains of structure and discipline. Given AI fairness' raison d'etre of "fairness", we argue that adopting intersectionality as an analytical framework is pivotal to effectively operationalizing fairness. Through a critical review of how intersectionality is discussed in 30 papers from the AI fairness literature, we deductively and inductively: 1) map how intersectionality tenets operate within the AI fairness paradigm and 2) uncover gaps between the conceptualization and operationalization of intersectionality. We find that researchers overwhelmingly reduce intersectionality to optimizing for fairness metrics over demographic subgroups. They also fail to discuss their social context and when mentioning power, they mostly situate it only within the AI pipeline. We: 3) outline and assess the implications of these gaps for critical inquiry and praxis, and 4) provide actionable recommendations for AI fairness researchers to engage with intersectionality in their work by grounding it in AI epistemology.

Large reasoning models achieve remarkable performance through extensive chain-of-thought generation, yet exhibit significant computational inefficiency by applying uniform reasoning strategies regardless of problem complexity. We present Hierarchical Budget Policy Optimization (HBPO), a reinforcement learning framework that enables models to learn problem-specific reasoning depths without sacrificing capability. HBPO addresses the fundamental challenge of exploration space collapse in efficiency-oriented training, where penalties on long output length systematically bias models away from necessary long reasoning paths. Through hierarchical budget exploration, our approach partitions rollout samples into multiple subgroups with distinct token budgets, aiming to enable efficient resource allocation while preventing degradation of capability. We introduce differentiated reward mechanisms that create budget-aware incentives aligned with the complexity of the problem, allowing models to discover natural correspondences between task requirements and computational effort. Extensive experiments demonstrate that HBPO reduces average token usage by up to 60.6% while improving accuracy by 3.14% across four reasoning benchmarks. Unlike existing methods that impose external constraints or rely on discrete mode selection, HBPO exhibits emergent adaptive behavior where models automatically adjust reasoning depth based on problem complexity. Our results suggest that reasoning efficiency and capability are not inherently conflicting, and can be simultaneously optimized through appropriately structured hierarchical training that preserves exploration diversity.

Reward modeling is a key step in building safe foundation models when applying reinforcement learning from human feedback (RLHF) to align Large Language Models (LLMs). However, reward modeling based on the Bradley-Terry (BT) model assumes a global reward function, failing to capture the inherently diverse and heterogeneous human preferences. Hence, such oversimplification limits LLMs from supporting personalization and pluralistic alignment. Theoretically, we show that when human preferences follow a mixture distribution of diverse subgroups, a single BT model has an irreducible error. While existing solutions, such as multi-objective learning with fine-grained annotations, help address this issue, they are costly and constrained by predefined attributes, failing to fully capture the richness of human values. In this work, we introduce MiCRo, a two-stage framework that enhances personalized preference learning by leveraging large-scale binary preference datasets without requiring explicit fine-grained annotations. In the first stage, MiCRo introduces context-aware mixture modeling approach to capture diverse human preferences. In the second stage, MiCRo integrates an online routing strategy that dynamically adapts mixture weights based on specific context to resolve ambiguity, allowing for efficient and scalable preference adaptation with minimal additional supervision. Experiments on multiple preference datasets demonstrate that MiCRo effectively captures diverse human preferences and significantly improves downstream personalization.

Computer vision models have been shown to exhibit and amplify biases across a wide array of datasets and tasks. Existing methods for quantifying bias in classification models primarily focus on dataset distribution and model performance on subgroups, overlooking the internal workings of a model. We introduce the Attention-IoU (Attention Intersection over Union) metric and related scores, which use attention maps to reveal biases within a model's internal representations and identify image features potentially causing the biases. First, we validate Attention-IoU on the synthetic Waterbirds dataset, showing that the metric accurately measures model bias. We then analyze the CelebA dataset, finding that Attention-IoU uncovers correlations beyond accuracy disparities. Through an investigation of individual attributes through the protected attribute of Male, we examine the distinct ways biases are represented in CelebA. Lastly, by subsampling the training set to change attribute correlations, we demonstrate that Attention-IoU reveals potential confounding variables not present in dataset labels.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

Large language models (LLMs) are increasingly essential in processing natural languages, yet their application is frequently compromised by biases and inaccuracies originating in their training data. In this study, we introduce Cross-Care, the first benchmark framework dedicated to assessing biases and real world knowledge in LLMs, specifically focusing on the representation of disease prevalence across diverse demographic groups. We systematically evaluate how demographic biases embedded in pre-training corpora like ThePile influence the outputs of LLMs. We expose and quantify discrepancies by juxtaposing these biases against actual disease prevalences in various U.S. demographic groups. Our results highlight substantial misalignment between LLM representation of disease prevalence and real disease prevalence rates across demographic subgroups, indicating a pronounced risk of bias propagation and a lack of real-world grounding for medical applications of LLMs. Furthermore, we observe that various alignment methods minimally resolve inconsistencies in the models' representation of disease prevalence across different languages. For further exploration and analysis, we make all data and a data visualization tool available at: www.crosscare.net.

For finite nilpotent groups J and N, suppose J acts on N via automorphisms. We exhibit a decomposition of the first cohomology set in terms of the first cohomologies of the Sylow p-subgroups of J that mirrors the primary decomposition of H^1(J,N) for abelian N. We then show that if N rtimes J acts on some non-empty set Omega, where the action of N is transitive and for each prime p a Sylow p-subgroup of J fixes an element of Omega, then J fixes an element of Omega.

To reduce the inference cost of large language models, model compression is increasingly used to create smaller scalable models. However, little is known about their robustness to minority subgroups defined by the labels and attributes of a dataset. In this paper, we investigate the effects of 18 different compression methods and settings on the subgroup robustness of BERT language models. We show that worst-group performance does not depend on model size alone, but also on the compression method used. Additionally, we find that model compression does not always worsen the performance on minority subgroups. Altogether, our analysis serves to further research into the subgroup robustness of model compression.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

In this work, we present DeFTAN-II, an efficient multichannel speech enhancement model based on transformer architecture and subgroup processing. Despite the success of transformers in speech enhancement, they face challenges in capturing local relations, reducing the high computational complexity, and lowering memory usage. To address these limitations, we introduce subgroup processing in our model, combining subgroups of locally emphasized features with other subgroups containing original features. The subgroup processing is implemented in several blocks of the proposed network. In the proposed split dense blocks extracting spatial features, a pair of subgroups is sequentially concatenated and processed by convolution layers to effectively reduce the computational complexity and memory usage. For the F- and T-transformers extracting temporal and spectral relations, we introduce cross-attention between subgroups to identify relationships between locally emphasized and non-emphasized features. The dual-path feedforward network then aggregates attended features in terms of the gating of local features processed by dilated convolutions. Through extensive comparisons with state-of-the-art multichannel speech enhancement models, we demonstrate that DeFTAN-II with subgroup processing outperforms existing methods at significantly lower computational complexity. Moreover, we evaluate the model's generalization capability on real-world data without fine-tuning, which further demonstrates its effectiveness in practical scenarios.

Visual recognition models are prone to learning spurious correlations induced by a biased training set where certain conditions B (\eg, Indoors) are over-represented in certain classes Y (\eg, Big Dogs). Synthetic data from off-the-shelf large-scale generative models offers a promising direction to mitigate this issue by augmenting underrepresented subgroups in the real dataset. However, by using a mixed distribution of real and synthetic data, we introduce another source of bias due to distributional differences between synthetic and real data (\eg synthetic artifacts). As we will show, prior work's approach for using synthetic data to resolve the model's bias toward B do not correct the model's bias toward the pair (B, G), where G denotes whether the sample is real or synthetic. Thus, the model could simply learn signals based on the pair (B, G) (\eg, Synthetic Indoors) to make predictions about Y (\eg, Big Dogs). To address this issue, we propose a simple, easy-to-implement, two-step training pipeline that we call From Fake to Real (FFR). The first step of FFR pre-trains a model on balanced synthetic data to learn robust representations across subgroups. In the second step, FFR fine-tunes the model on real data using ERM or common loss-based bias mitigation methods. By training on real and synthetic data separately, FFR does not expose the model to the statistical differences between real and synthetic data and thus avoids the issue of bias toward the pair (B, G). Our experiments show that FFR improves worst group accuracy over the state-of-the-art by up to 20\% over three datasets. Code available: https://github.com/mqraitem/From-Fake-to-Real

In this paper, we provide 20,000 non-trivial human annotations on popular datasets as a first step to bridge gap to studying how natural semantic spurious features affect image classification, as prior works often study datasets mixing low-level features due to limitations in accessing realistic datasets. We investigate how natural background colors play a role as spurious features by annotating the test sets of CIFAR10 and CIFAR100 into subgroups based on the background color of each image. We name our datasets CIFAR10-B and CIFAR100-B and integrate them with CIFAR-Cs. We find that overall human-level accuracy does not guarantee consistent subgroup performances, and the phenomenon remains even on models pre-trained on ImageNet or after data augmentation (DA). To alleviate this issue, we propose FlowAug, a semantic DA that leverages decoupled semantic representations captured by a pre-trained generative flow. Experimental results show that FlowAug achieves more consistent subgroup results than other types of DA methods on CIFAR10/100 and on CIFAR10/100-C. Additionally, it shows better generalization performance. Furthermore, we propose a generic metric, MacroStd, for studying model robustness to spurious correlations, where we take a macro average on the weighted standard deviations across different classes. We show MacroStd being more predictive of better performances; per our metric, FlowAug demonstrates improvements on subgroup discrepancy. Although this metric is proposed to study our curated datasets, it applies to all datasets that have subgroups or subclasses. Lastly, we also show superior out-of-distribution results on CIFAR10.1.

Machine learning models for medical image analysis often suffer from poor performance on important subsets of a population that are not identified during training or testing. For example, overall performance of a cancer detection model may be high, but the model still consistently misses a rare but aggressive cancer subtype. We refer to this problem as hidden stratification, and observe that it results from incompletely describing the meaningful variation in a dataset. While hidden stratification can substantially reduce the clinical efficacy of machine learning models, its effects remain difficult to measure. In this work, we assess the utility of several possible techniques for measuring and describing hidden stratification effects, and characterize these effects on multiple medical imaging datasets. We find evidence that hidden stratification can occur in unidentified imaging subsets with low prevalence, low label quality, subtle distinguishing features, or spurious correlates, and that it can result in relative performance differences of over 20% on clinically important subsets. Finally, we explore the clinical implications of our findings, and suggest that evaluation of hidden stratification should be a critical component of any machine learning deployment in medical imaging.

The growing capability and accessibility of machine learning has led to its application to many real-world domains and data about people. Despite the benefits algorithmic systems may bring, models can reflect, inject, or exacerbate implicit and explicit societal biases into their outputs, disadvantaging certain demographic subgroups. Discovering which biases a machine learning model has introduced is a great challenge, due to the numerous definitions of fairness and the large number of potentially impacted subgroups. We present FairVis, a mixed-initiative visual analytics system that integrates a novel subgroup discovery technique for users to audit the fairness of machine learning models. Through FairVis, users can apply domain knowledge to generate and investigate known subgroups, and explore suggested and similar subgroups. FairVis' coordinated views enable users to explore a high-level overview of subgroup performance and subsequently drill down into detailed investigation of specific subgroups. We show how FairVis helps to discover biases in two real datasets used in predicting income and recidivism. As a visual analytics system devoted to discovering bias in machine learning, FairVis demonstrates how interactive visualization may help data scientists and the general public understand and create more equitable algorithmic systems.

Error slice discovery is crucial to diagnose and mitigate model errors. Current clustering or discrete attribute-based slice discovery methods face key limitations: 1) clustering results in incoherent slices, while assigning discrete attributes to slices leads to incomplete coverage of error patterns due to missing or insufficient attributes; 2) these methods lack complex reasoning, preventing them from fully explaining model biases; 3) they fail to integrate domain knowledge, limiting their usage in specialized fields \eg radiology. We propose\ladder (Language-Driven Discovery and Error Rectification), to address the limitations by: (1) leveraging the flexibility of natural language to address incompleteness, (2) employing LLM's latent domain knowledge and advanced reasoning to analyze sentences and derive testable hypotheses directly, identifying biased attributes, and form coherent error slices without clustering. Existing mitigation methods typically address only the worst-performing group, often amplifying errors in other subgroups. In contrast,\ladder generates pseudo attributes from the discovered hypotheses to mitigate errors across all biases without explicit attribute annotations or prior knowledge of bias. Rigorous evaluations on 6 datasets spanning natural and medical images -- comparing 200+ classifiers with diverse architectures, pretraining strategies, and LLMs -- show that\ladder consistently outperforms existing baselines in discovering and mitigating biases.

Training models with robust group fairness properties is crucial in ethically sensitive application areas such as medical diagnosis. Despite the growing body of work aiming to minimise demographic bias in AI, this problem remains challenging. A key reason for this challenge is the fairness generalisation gap: High-capacity deep learning models can fit all training data nearly perfectly, and thus also exhibit perfect fairness during training. In this case, bias emerges only during testing when generalisation performance differs across subgroups. This motivates us to take a bi-level optimisation perspective on fair learning: Optimising the learning strategy based on validation fairness. Specifically, we consider the highly effective workflow of adapting pre-trained models to downstream medical imaging tasks using parameter-efficient fine-tuning (PEFT) techniques. There is a trade-off between updating more parameters, enabling a better fit to the task of interest vs. fewer parameters, potentially reducing the generalisation gap. To manage this tradeoff, we propose FairTune, a framework to optimise the choice of PEFT parameters with respect to fairness. We demonstrate empirically that FairTune leads to improved fairness on a range of medical imaging datasets. The code is available at https://github.com/Raman1121/FairTune

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

While research on applications and evaluations of explanation methods continues to expand, fairness of the explanation methods concerning disparities in their performance across subgroups remains an often overlooked aspect. In this paper, we address this gap by showing that, across three tasks and five language models, widely used post-hoc feature attribution methods exhibit significant gender disparity with respect to their faithfulness, robustness, and complexity. These disparities persist even when the models are pre-trained or fine-tuned on particularly unbiased datasets, indicating that the disparities we observe are not merely consequences of biased training data. Our results highlight the importance of addressing disparities in explanations when developing and applying explainability methods, as these can lead to biased outcomes against certain subgroups, with particularly critical implications in high-stakes contexts. Furthermore, our findings underscore the importance of incorporating the fairness of explanations, alongside overall model fairness and explainability, as a requirement in regulatory frameworks.

Let F in S_{k_1}(Gamma^{(2)}(N_1)) and G in S_{k_2}(Gamma^{(2)}(N_2)) be two Siegel cusp forms over the congruence subgroups Gamma^{(2)}(N_1) and Gamma^{(2)}(N_2) respectively. Assume that they are Hecke eigenforms in different eigenspaces and satisfy the Generalized Ramanujan Conjecture. Let lambda_F(p) denote the eigenvalue of F with respect to the Hecke operator T(p). In this article, we compute a lower bound for the density of the set of primes, { p : lambda_F(p) lambda_G(p) < 0 }.

The Fair Graph Anomaly Detection (FairGAD) problem aims to accurately detect anomalous nodes in an input graph while ensuring fairness and avoiding biased predictions against individuals from sensitive subgroups such as gender or political leanings. Fairness in graphs is particularly crucial in anomaly detection areas such as misinformation detection in search/ranking systems, where decision outcomes can significantly affect individuals. However, the current literature does not comprehensively discuss this problem, nor does it provide realistic datasets that encompass actual graph structures, anomaly labels, and sensitive attributes for research in FairGAD. To bridge this gap, we introduce a formal definition of the FairGAD problem and present two novel graph datasets constructed from the globally prominent social media platforms Reddit and Twitter. These datasets comprise 1.2 million and 400,000 edges associated with 9,000 and 47,000 nodes, respectively, and leverage political leanings as sensitive attributes and misinformation spreaders as anomaly labels. We demonstrate that our FairGAD datasets significantly differ from the synthetic datasets used currently by the research community. These new datasets offer significant values for FairGAD by providing realistic data that captures the intricacies of social networks. Using our datasets, we investigate the performance-fairness trade-off in eleven existing GAD and non-graph AD methods on five state-of-the-art fairness methods, which sheds light on their effectiveness and limitations in addressing the FairGAD problem.

Expected Goals (xG) has emerged as a popular tool for evaluating finishing skill in soccer analytics. It involves comparing a player's cumulative xG with their actual goal output, where consistent overperformance indicates strong finishing ability. However, the assessment of finishing skill in soccer using xG remains contentious due to players' difficulty in consistently outperforming their cumulative xG. In this paper, we aim to address the limitations and nuances surrounding the evaluation of finishing skill using xG statistics. Specifically, we explore three hypotheses: (1) the deviation between actual and expected goals is an inadequate metric due to the high variance of shot outcomes and limited sample sizes, (2) the inclusion of all shots in cumulative xG calculation may be inappropriate, and (3) xG models contain biases arising from interdependencies in the data that affect skill measurement. We found that sustained overperformance of cumulative xG requires both high shot volumes and exceptional finishing, including all shot types can obscure the finishing ability of proficient strikers, and that there is a persistent bias that makes the actual and expected goals closer for excellent finishers than it really is. Overall, our analysis indicates that we need more nuanced quantitative approaches for investigating a player's finishing ability, which we achieved using a technique from AI fairness to learn an xG model that is calibrated for multiple subgroups of players. As a concrete use case, we show that (1) the standard biased xG model underestimates Messi's GAX by 17% and (2) Messi's GAX is 27% higher than the typical elite high-shot-volume attacker, indicating that Messi is even a more exceptional finisher than people commonly believed.

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard.

Knee Osteoarthritis (KOA) is a highly prevalent chronic musculoskeletal condition with no currently available treatment. The manifestation of KOA is heterogeneous and prediction of its progression is challenging. Current literature suggests that the use of multi-modal data and advanced modeling methods, such as the ones based on Deep Learning, has promise in tackling this challenge. To date, however, the evidence on the efficacy of this approach is limited. In this study, we leveraged recent advances in Deep Learning and, using a Transformer approach, developed a unified framework for the multi-modal fusion of knee imaging data. Subsequently, we analyzed its performance across a range of scenarios by investigating multiple progression horizons -- from short-term to long-term. We report our findings using a large cohort (n=2421-3967) derived from the Osteoarthritis Initiative dataset. We show that structural knee MRI allows identifying radiographic KOA progressors on par with multi-modal fusion approaches, achieving an area under the ROC curve (ROC AUC) of 0.70-0.76 and Average Precision (AP) of 0.15-0.54 in 2-8 year horizons. Progression within 1 year was better predicted with a multi-modal method using X-ray, structural, and compositional MR images -- ROC AUC of 0.76(0.04), AP of 0.13(0.04) -- or via clinical data. Our follow-up analysis generally shows that prediction from the imaging data is more accurate for post-traumatic subjects, and we further investigate which subject subgroups may benefit the most. The present study provides novel insights into multi-modal imaging of KOA and brings a unified data-driven framework for studying its progression in an end-to-end manner, providing new tools for the design of more efficient clinical trials. The source code of our framework and the pre-trained models are made publicly available.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Recent advances in Natural Language Processing (NLP), and specifically automated Question Answering (QA) systems, have demonstrated both impressive linguistic fluency and a pernicious tendency to reflect social biases. In this study, we introduce Q-Pain, a dataset for assessing bias in medical QA in the context of pain management, one of the most challenging forms of clinical decision-making. Along with the dataset, we propose a new, rigorous framework, including a sample experimental design, to measure the potential biases present when making treatment decisions. We demonstrate its use by assessing two reference Question-Answering systems, GPT-2 and GPT-3, and find statistically significant differences in treatment between intersectional race-gender subgroups, thus reaffirming the risks posed by AI in medical settings, and the need for datasets like ours to ensure safety before medical AI applications are deployed.

Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics.

Reinforcement Learning from Human Feedback (RLHF) is a powerful paradigm for aligning foundation models to human values and preferences. However, current RLHF techniques cannot account for the naturally occurring differences in individual human preferences across a diverse population. When these differences arise, traditional RLHF frameworks simply average over them, leading to inaccurate rewards and poor performance for individual subgroups. To address the need for pluralistic alignment, we develop a class of multimodal RLHF methods. Our proposed techniques are based on a latent variable formulation - inferring a novel user-specific latent and learning reward models and policies conditioned on this latent without additional user-specific data. While conceptually simple, we show that in practice, this reward modeling requires careful algorithmic considerations around model architecture and reward scaling. To empirically validate our proposed technique, we first show that it can provide a way to combat underspecification in simulated control problems, inferring and optimizing user-specific reward functions. Next, we conduct experiments on pluralistic language datasets representing diverse user preferences and demonstrate improved reward function accuracy. We additionally show the benefits of this probabilistic framework in terms of measuring uncertainty, and actively learning user preferences. This work enables learning from diverse populations of users with divergent preferences, an important challenge that naturally occurs in problems from robot learning to foundation model alignment.

Recent advancements in conversational AI have created an urgent need for safety guardrails that prevent users from being exposed to offensive and dangerous content. Much of this work relies on human ratings and feedback, but does not account for the fact that perceptions of offense and safety are inherently subjective and that there may be systematic disagreements between raters that align with their socio-demographic identities. Instead, current machine learning approaches largely ignore rater subjectivity and use gold standards that obscure disagreements (e.g., through majority voting). In order to better understand the socio-cultural leanings of such tasks, we propose a comprehensive disagreement analysis framework to measure systematic diversity in perspectives among different rater subgroups. We then demonstrate its utility by applying this framework to a dataset of human-chatbot conversations rated by a demographically diverse pool of raters. Our analysis reveals specific rater groups that have more diverse perspectives than the rest, and informs demographic axes that are crucial to consider for safety annotations.

We propose an experimental method for measuring bias in face recognition systems. Existing methods to measure bias depend on benchmark datasets that are collected in the wild and annotated for protected (e.g., race, gender) and non-protected (e.g., pose, lighting) attributes. Such observational datasets only permit correlational conclusions, e.g., "Algorithm A's accuracy is different on female and male faces in dataset X.". By contrast, experimental methods manipulate attributes individually and thus permit causal conclusions, e.g., "Algorithm A's accuracy is affected by gender and skin color." Our method is based on generating synthetic faces using a neural face generator, where each attribute of interest is modified independently while leaving all other attributes constant. Human observers crucially provide the ground truth on perceptual identity similarity between synthetic image pairs. We validate our method quantitatively by evaluating race and gender biases of three research-grade face recognition models. Our synthetic pipeline reveals that for these algorithms, accuracy is lower for Black and East Asian population subgroups. Our method can also quantify how perceptual changes in attributes affect face identity distances reported by these models. Our large synthetic dataset, consisting of 48,000 synthetic face image pairs (10,200 unique synthetic faces) and 555,000 human annotations (individual attributes and pairwise identity comparisons) is available to researchers in this important area.

This paper addresses the challenge of grading visual features in lumbar spine MRI using Deep Learning. Such a method is essential for the automatic quantification of structural changes in the spine, which is valuable for understanding low back pain. Multiple recent studies investigated different architecture designs, and the most recent success has been attributed to the use of transformer architectures. In this work, we argue that with a well-tuned three-stage pipeline comprising semantic segmentation, localization, and classification, convolutional networks outperform the state-of-the-art approaches. We conducted an ablation study of the existing methods in a population cohort, and report performance generalization across various subgroups. Our code is publicly available to advance research on disc degeneration and low back pain.

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorization of the training data also presents significant privacy risks when the training data contains sensitive personal information and thus it is important to understand whether such memorization is necessary for accurate learning. We provide the first conceptual explanation and a theoretical model for this phenomenon. Specifically, we demonstrate that for natural data distributions memorization of labels is necessary for achieving close-to-optimal generalization error. Crucially, even labels of outliers and noisy labels need to be memorized. The model is motivated and supported by the results of several recent empirical works. In our model, data is sampled from a mixture of subpopulations and our results show that memorization is necessary whenever the distribution of subpopulation frequencies is long-tailed. Image and text data is known to be long-tailed and therefore our results establish a formal link between these empirical phenomena. Our results allow to quantify the cost of limiting memorization in learning and explain the disparate effects that privacy and model compression have on different subgroups.