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Deep Learning · Theory

Ruichen Xu, Kexin Chen

Recent theoretical studies (Kou et al., 2023; Cao et al., 2022) revealed a sharp phase transition from benign to harmful overfitting when thenoise-to-feature ratio exceeds a threshold—a situation common in long-tailed data distributions where atypical data is prevalent. However, such harmful overfitting rarely happens in overparameterized neural networks. Further experimental results suggested that memorization is necessary for achieving near-optimal generalization error in long-tailed data distributions (Feldman & Zhang, 2020). We argue that this discrepancy between theoretical predictions and empirical observations arises because previous feature-noise data models overlook the heterogeneous nature of noise across different data classes. In this paper, we refine the feature-noise data model by incorporating class-dependent heterogeneous noise and re-examine the overfitting phenomenon in neural networks. Through a comprehensive analysis of the training dynamics, we establish test loss bounds for the refined model. Our findings reveal that neural networks can leverage "data noise" to learn implicit features that improve the classification accuracy for long-tailed data. Our analysis also provides a training-free metric for evaluating data influence on test performance. Experimental validation on both synthetic and real-world datasets supports our theoretical results.

Applications · Computer Vision

Deyu Bo, Xinchao Wang

This study introduces dataset distillation (DD) tailored for 3D data, particularly point clouds. DD aims to substitute large-scale real datasets with a small set of synthetic samples while preserving model performance. Existing methods mainly focus on structured data such as images. However, adapting DD for unstructured point clouds poses challenges due to their diverse orientations and resolutions in 3D space. To address these challenges, we theoretically demonstrate the importance of matching rotation-invariant features between real and synthetic data for 3D distillation. We further propose a plug-and-play point cloud rotator to align the point cloud to a canonical orientation, facilitating the learning of rotation-invariant features by all point cloud models. Furthermore, instead of optimizing fixed-size synthetic data directly, we devise a point-wise generator to produce point clouds at various resolutions based on the sampled noise amount. Compared to conventional DD methods, the proposed approach, termed DD3D, enables efficient training on low-resolution point clouds while generating high-resolution data for evaluation, thereby significantly reducing memory requirements and enhancing model scalability. Extensive experiments validate the effectiveness of DD3D in shape classification and part segmentation tasks across diverse scenarios, such as cross-architecture and cross-resolution settings.

Optimization

Vincent Roulet, Tianlin Liu, Nino Vieillard, Michael Sander, Mathieu Blondel

The logistic loss (a.k.a. cross-entropy loss) is one of the most popular loss functions used for multiclass classification. It is also the loss function of choice for next-token prediction in language modeling. It is associated with the Kullback-Leibler (KL) divergence and the softargmax operator. In this work, we propose to construct new convex loss functions based on $f$-divergences. Our loss functions generalize the logistic loss in two directions: i) by replacing the KL divergence with $f$-divergences and ii) by allowing non-uniform reference measures. We instantiate our framework for numerous $f$-divergences, recovering existing losses and creating new ones.By analogy with the logistic loss, the loss function generated by an $f$-divergence is associated with an operator, that we dub $f$-softargmax. We derive a novel parallelizable bisection algorithm for computing the $f$-softargmax associated with any $f$-divergence.On the empirical side, one of the goals of this paper is to determine the effectiveness of loss functions beyond the classical cross-entropy in a language model setting, including on pre-training, post-training (SFT) and distillation. We show that the loss function generated by the $\alpha$-divergence (which is equivalent to Tsallis $\alpha$-negentropy in the case of unit reference measures) with $\alpha=1.5$ performs well across several tasks.

Deep Learning · Attention Mechanisms

Jerome Garnier-Brun, Marc Mezard, Emanuele Moscato, Luca Saglietti

Understanding the learning process and the embedded computation in transformers is becoming a central goal for the development of interpretable AI. In the present study, we introduce a hierarchical filtering procedure for data models of sequences on trees, allowing us to hand-tune the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformers can approximate the exact inference algorithm when trained on root classification and masked language modeling tasks, and study *how* this computation is discovered and implemented. We find that correlations at larger distances, corresponding to increasing layers of the hierarchy, are sequentially included by the network during training. By comparing attention maps from models trained with varying degrees of filtering and by probing the different encoder levels, we find clear evidence of a reconstruction of correlations on successive length scales corresponding to the various levels of the hierarchy, which we relate to a plausible implementation of the exact inference algorithm within the same architecture.

Deep Learning · Robustness

Mohamad Chehade, Wenting Li, Brian Bell, Russell Bent, Saif Kazi, Hao Zhu

The robustness of neural networks is crucial in safety-critical applications, where identifying a reliable input space is essential for effective model selection, robustness evaluation, and the development of reliable control strategies. Most existing robustness verification methods assess the worst-case output under the assumption that the input space is known. However, precisely identifying a verifiable input space $ \mathcal{C} $, where no adversarial examples exist, is challenging due to the possible high dimensionality, discontinuity, and non-convex nature of the input space. To address this challenge, we propose a novel framework, **LEVIS**, comprising **LEVIS-$\alpha$** and **LEVIS-$\beta$**. **LEVIS-$\alpha$** identifies a single, large verifiable ball that intersects at least two boundaries of a bounded region $ \mathcal{C} $, while **LEVIS-$\beta$** systematically captures the entirety of the verifiable space by integrating multiple verifiable balls. Our contributions are fourfold: we introduce a verification framework, **LEVIS**, incorporating two optimization techniques for computing nearest and directional adversarial points based on mixed-integer programming (MIP); to enhance scalability, we integrate complementary constrained (CC) optimization with a reduced MIP formulation, achieving up to a 17-fold reduction in runtime by approximating the verifiable region in a principled way; we provide a theoretical analysis characterizing the properties of the verifiable balls obtained through **LEVIS-$\alpha$**; and we validate our approach across diverse applications, including electrical power flow regression and image classification, demonstrating performance improvements and visualizing the geometric properties of the verifiable region.

Theory · Online Learning and Bandits

Martino Bernasconi, Andrea Celli, Riccardo Colini Baldeschi, Federico Fusco, Stefano Leonardi, Matteo Russo

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is *asymptotically* equivalent to a stochastic i.i.d.~one, but, for finite times, it may exhibit significant *non-stationarity*, which can hinder the performance of stochastic learning algorithms.While algorithms for adversarial inputs naturally maintain their regret guarantees in random order, simple no-regret algorithms exist for the stochastic model that fail against random-order instances. In this paper, we propose a general procedure to adapt stochastic learning algorithms to the random-order model without substantially affecting their regret guarantees. This allows us to recover improved regret bounds for prediction with delays, bandits with switching costs, and online learning with constraints. Finally, we investigate online classification and prove that, in random order, learnability is characterized by the VC dimension rather than by the Littlestone dimension, thus providing a further separation from the general adversarial model.

Social Aspects · Privacy

Conor Snedeker, Xinyu Zhou, Raef Bassily

We study model personalization under user-level differential privacy (DP) in the shared representation framework. In this problem, there are $n$ users whose data is statistically heterogeneous, and their optimal parameters share an unknown embedding $U^* \in\mathbb{R}^{d\times k}$ that maps the user parameters in $\mathbb{R}^d$ to low-dimensional representations in $\mathbb{R}^k$, where $k\ll d$. Our goal is to privately recover the shared embedding and the local low-dimensional representations with small excess risk in the federated setting. We propose a private, efficient federated learning algorithm to learn the shared embedding based on the FedRep algorithm in (Collins et al.,2021). Unlike (Collins et al., 2021), our algorithm satisfies differential privacy, and our results hold for the case of noisy labels. In contrast to prior work on private model personalization (Jain et al., 2021), our utility guarantees hold under a larger class of users' distributions (sub-Gaussian instead of Gaussian distributions). Additionally, in natural parameter regimes, we improve the privacy error term in (Jainet al., 2021) by a factor of $\widetilde{O}(dk)$. Next, we consider the binary classification setting. We present an information-theoretic construction to privately learn the shared embedding and derive a margin-based accuracy guarantee that is independent of $d$. Our method utilizes the Johnson-Lindenstrauss transform to reduce the effective dimensions of the shared embedding and the users' data. This result shows that dimension-independent risk bounds are possible in this setting under a margin loss.

Deep Learning · Robustness

Junhao Dong, Piotr Koniusz, Yifei Zhang, Hao Zhu, Weiming Liu, Xinghua Qu, Yew Soon ONG

Vision-Language Models (VLMs) such as CLIP excel at zero-shot classification due to large-scale pre-training but are vulnerable to adversarial examples. Adversarial fine-tuning robustifies zero-shot models by aligning prediction scores of individual adversaries with their clean counterparts, which typically overlooks intermediate adversarial samples along the adversarial trajectory crossing the decision boundary. Such intermediate adversaries and their vicinity produce informative representations capturing the decision boundary in detail. They can be improved by sampling adversarial candidates from simplices formed by joining two consecutive vertices on the adversarial trajectory and their clean counterpart. However, sampling simplices for adversaries is very costly. To train robust VLM, we overcome these limitations by Taylor expansion and formulating an upper-bound of alignment loss that depends on the Jacobian/Hessian obtained at clean samples. As regions between clean and intermediate adversarial samples capture a larger decision landscape, we robustify VLM by plausible adversaries from simplices by our closed-form formulation equivalent to infinite uniform sampling of the simplex. We obtain state-of-the-art robustness across 15 datasets and diverse vision-language tasks.

Applications · Everything Else

Xiang Zhang, Jiaqi Wei, Zijie Qiu, Sheng Xu, Nanqing Dong, ZhiQiang Gao, Siqi Sun

Peptide sequencing—the process of identifying amino acid sequences from mass spectrometry data—is a fundamental task in proteomics. Non-Autoregressive Transformers (NATs) have proven highly effective for this task, outperforming traditional methods. Unlike autoregressive models, which generate tokens sequentially, NATs predict all positions simultaneously, leveraging bidirectional context through unmasked self-attention.However, existing NAT approaches often rely on Connectionist Temporal Classification (CTC) loss, which presents significant optimization challenges due to CTC's complexity and increases the risk of training failures. To address these issues, we propose an improved non-autoregressive peptide sequencing model that incorporates a structured protein sequence curriculum learning strategy. This approach adjusts protein's learning difficulty based on the model’s estimated protein generational capabilities through a sampling process, progressively learning peptide generation from simple to complex sequences. Additionally, we introduce a self-refining inference-time module that iteratively enhances predictions using learned NAT token embeddings, improving sequence accuracy at a fine-grained level. Our curriculum learning strategy reduces NAT training failures frequency by more than 90% based on sampled training over various data distributions. Evaluations on nine benchmark species demonstrate that our approach outperforms all previous methods across multiple metrics and species. Model and source code are available at https://github.com/BEAM-Labs/denovo.

General Machine Learning · Supervised Learning

Teng Huang, Bin-Bin Jia, Min-Ling Zhang

In multi-dimensional classification (MDC), the semantics of objects are characterized by multiple class variables from different dimensions. Existing MDC approaches focus on designing effective class dependency modeling strategies to enhance classification performance. However, the intercoupling of multiple class variables poses a significant challenge to the precise modeling of class dependencies. In this paper, we make the first attempt towards escaping from class dependency modeling for addressing MDC problems. Accordingly, a novel MDC approach named DCOM is proposed by decoupling the interactions of different dimensions in MDC. Specifically, DCOM endeavors to identify a latent factor that encapsulates the most salient and critical feature information. This factor will facilitate partial conditional independence among class variables conditioned on both the original feature vector and the learned latent embedding. Once the conditional independence is established, classification models can be readily induced by employing simple neural networks on each dimension. Extensive experiments conducted on benchmark data sets demonstrate that DCOM outperforms other state-of-the-art MDC approaches.

Theory · Learning Theory

Gholamali Aminian, Amir R. Asadi, Tian Li, Ahmad Beirami, Gesine Reinert, Samuel Cohen

The generalization error (risk) of a supervised statistical learning algorithm quantifies its prediction ability on previously unseen data. Inspired by exponential tilting, Li et al. (2021) proposed the {\it tilted empirical risk} (TER) as a non-linear risk metric for machine learning applications such as classification and regression problems. In this work, we examine the generalization error of the tilted empirical risk in the robustness regime under \textit{negative tilt}. Our first contribution is to provide uniform and information-theoretic bounds on the {\it tilted generalization error}, defined as the difference between the population risk and the tilted empirical risk, under negative tilt for unbounded loss function under bounded $(1+\epsilon)$-th moment of loss function for some $\epsilon\in(0,1]$ with a convergence rate of $O(n^{-\epsilon/(1+\epsilon)})$ where $n$ is the number of training samples, revealing a novel application for TER under no distribution shift. Secondly, we study the robustness of the tilted empirical risk with respect to noisy outliers at training time and provide theoretical guarantees under distribution shift for the tilted empirical risk. We empirically corroborate our findings in simple experimental setups where we evaluate our bounds to select the value of tilt in a data-driven manner.

Applications · Neuroscience, Cognitive Science

Abdulkadir Gokce, Martin Schrimpf

When trained on large-scale object classification datasets, certain artificial neural network models begin to approximate core object recognition behaviors and neural response patterns in the primate brain. While recent machine learning advances suggest that scaling compute, model size, and dataset size improves task performance, the impact of scaling on brain alignment remains unclear. In this study, we explore scaling laws for modeling the primate visual ventral stream by systematically evaluating over 600 models trained under controlled conditions on benchmarks spanning V1, V2, V4, IT and behavior. We find that while behavioral alignment continues to scale with larger models, neural alignment saturates. This observation remains true across model architectures and training datasets, even though models with stronger inductive biases and datasets with higher-quality images are more compute-efficient. Increased scaling is especially beneficial for higher-level visual areas, where small models trained on few samples exhibit only poor alignment. Our results suggest that while scaling current architectures and datasets might suffice for alignment with human core object recognition behavior, it will not yield improved models of the brain's visual ventral stream, highlighting the need for novel strategies in building brain models.

General Machine Learning · Everything Else

Florence Regol, Leo Schwinn, Kyle Sprague, Mark Coates, Thomas L Markovich

A significant challenge in maintaining real-world machine learning models is responding to the continuous and unpredictable evolution of data. Most practitioners are faced with the difficult question: when should I retrain or update my machine learning model? This seemingly straightforward problem is particularly challenging for three reasons: 1) decisions must be made based on very limited information - we usually have access to only a few examples, 2) the nature, extent, and impact of the distribution shift are unknown, and 3) it involves specifying a cost ratio between retraining and poor performance, which can be hard to characterize. Existing works address certain aspects of this problem, but none offer a comprehensive solution. Distribution shift detection falls short as it cannot account for the cost trade-off; the scarcity of the data, paired with its unusual structure, makes it a poor fit for existing offline reinforcement learning methods, and the online learning formulation overlooks key practical considerations. To address this, we present a principled formulation of the retraining problem and propose an uncertainty-based method that makes decisions by continually forecasting the evolution of model performance evaluated with a bounded metric. Our experiments, addressing classification tasks, show that the method consistently outperforms existing baselines on 7 datasets. We thoroughly assess its robustness to varying cost trade-off values and mis-specified cost trade-offs.

Optimization · Stochastic

Jindong Tong, Hongcheng Liu, Johannes Royset

This paper focuses on non-asymptotic confidence bounds (CB) for the optimal values of stochastic optimization (SO) problems. Existing approaches often rely on two conditions that may be restrictive: The need for a global Lipschitz constant and the assumption of light-tailed distributions. Beyond either of the conditions, it remains largely unknown whether computable CBs can be constructed. In view of this literature gap, we provide three key findings below: (i) Based on the conventional formulation of sample average approximation (SAA), we derive non-Lipschitzian CBs for convex SP problems under heavy tails. (ii) We explore diametrical risk minimization (DRM)---a recently introduced modification to SAA---and attain non-Lipschitzian CBs for nonconvex SP problems in light-tailed settings. (iii) We extend our analysis of DRM to handle heavy-tailed randomness by utilizing properties in formulations for training over-parameterized classification models.

Social Aspects · Accountability, Transparency, and Interpretability

Wei Liu, Zhongyu Niu, Lang Gao, Zhiying Deng, Jun Wang, Haozhao Wang, Ruixuan Li

This study investigates the self-rationalization framework constructed with a cooperative game, where a generator initially extracts the most informative segment from raw input, and a subsequent predictor utilizes the selected subset for its input. The generator and predictor are trained collaboratively to maximize prediction accuracy. In this paper, we first uncover a potential caveat: such a cooperative game could unintentionally introduce a sampling bias during rationale extraction. Specifically, the generator might inadvertently create an incorrect correlation between the selected rationale candidate and the label, even when they are semantically unrelated in the original dataset. Subsequently, we elucidate the origins of this bias using both detailed theoretical analysis and empirical evidence. Our findings suggest a direction for inspecting these correlations through attacks, based on which we further introduce an instruction to prevent the predictor from learning the correlations.Through experiments on six text classification datasets and two graph classification datasets using three network architectures (GRUs, BERT, and GCN), we show that our method significantly outperforms recent rationalization methods.

General Machine Learning · Transfer, Multitask and Meta-learning

Yulun Wu, Doron Bergman

We present an Adversarially Pre-trained Transformer (APT) that is able to perform zero-shot meta-learning on tabular prediction tasks without using any real-world dataset to pre-train the model, extending on the recent development of Prior-Data Fitted Networks (PFNs) and TabPFN. Specifically, APT is pre-trained with adversarial synthetic data agents, who continue to shift their underlying data generating distribution and deliberately challenge the model with different synthetic datasets. In addition, we propose a mixture block model architecture that is able to handle classification tasks with arbitrary number of classes, addressing the class size limitation -- a crucial weakness of prior tabular zero-shot learning algorithms. In experiments, we show that our framework matches state-of-the-art performance on small tabular classification tasks without filtering on dataset characteristics such as number of classes and number of missing values, while maintaining an average runtime under one second. On common benchmark dataset suites in both classification and regression, we show that adversarial pre-training was able to enhance TabPFN's performance. In our analysis, we demonstrate that the adversarial synthetic data agents were able to generate a more diverse collection of data compared to the ordinary random generator in TabPFN. In addition, we demonstrate that our mixture block neural design has improved generalizability and greatly accelerated pre-training.

Theory · Deep Learning

Zeqiong Lv, Chao Qian, Yun Liu, Jiahao Fan, Yanan Sun

Evolutionary neural architecture search (ENAS) is a key part of evolutionary machine learning, which commonly utilizes evolutionary algorithms (EAs) to automatically design high-performing deep neural architectures. During past years, various ENAS methods have been proposed with exceptional performance. However, the theory research of ENAS is still in the infant. In this work, we step for the runtime analysis, which is an essential theory aspect of EAs, of ENAS upon multiclass classification problems. Specifically, we first propose a benchmark to lay the groundwork for the analysis. Furthermore, we design a two-level search space, making it suitable for multiclass classification problems and consistent with the common settings of ENAS. Based on both designs, we consider (1+1)-ENAS algorithms with one-bit and bit-wise mutations, and analyze their upper and lower bounds on the expected runtime. We prove that the algorithm using both mutations can find the optimum with the expected runtime upper bound of $O(rM\ln{rM})$ and lower bound of $\Omega(rM\ln{M})$. This suggests that a simple one-bit mutation may be greatly considered, given that most state-of-the-art ENAS methods are laboriously designed with the bit-wise mutation. Empirical studies also support our theoretical proof.

Social Aspects · Accountability, Transparency, and Interpretability

Feifei Li, Mi Zhang, Zhaoxiang Wang, Min Yang

Interpretability of point cloud (PC) models becomes imperative given their deployment in safety-critical scenarios such as autonomous vehicles. We focus on attributing PC model outputs to interpretable critical concepts, defined as meaningful subsets of the input point cloud.To enable human-understandable diagnostics of model failures, an ideal critical subset should be *faithful* (preserving points that causally influence predictions) and *conceptually coherent* (forming semantically meaningful structures that align with human perception).We propose InfoCons, an explanation framework that applies information-theoretic principles to decompose the point cloud into 3D concepts, enabling the examination of their causal effect on model predictions with learnable priors.We evaluate InfoCons on synthetic datasets for classification, comparing it qualitatively and quantitatively with four baselines. We further demonstrate its scalability and flexibility on two real-world datasets and in two applications that utilize critical scores of PC.

General Machine Learning · Evaluation

Roman Plaud, Alexandre Perez-Lebel, Matthieu Labeau, Antoine Saillenfest, Thomas Bonald

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respectto a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a *subset of nodes*, we focus on rules dedicated to the hierarchical $\mathrm{hF}_{\beta}$ scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conductextensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications.

Social Aspects · Accountability, Transparency, and Interpretability

Robert Geirhos, Priyank Jaini, Austin Stone, Sourabh Medapati, Xi Yi, George Toderici, Abhijit Ogale, Jonathon Shlens

Training a neural network is a monolithic endeavor, akin to carving knowledge into stone: once the process is completed, editing the knowledge in a network is nearly impossible, since all information is distributed across the network's weights. We here explore a simple, compelling alternative by marrying the representational power of deep neural networks with the flexibility of a database. Decomposing the task of image classification into image similarity (from a pre-trained embedding) and search (via fast nearest neighbor retrieval from a knowledge database), we build a simple and flexible visual memory that has the following key capabilities: (1.) The ability to flexibly add data across scales: from individual samples all the way to entire classes and billion-scale data; (2.) The ability to remove data through unlearning and memory pruning; (3.) An interpretable decision-mechanism on which we can intervene to control its behavior. Taken together, these capabilities comprehensively demonstrate the benefits of an explicit visual memory. We hope that it might contribute to a conversation on how knowledge should be represented in deep vision models---beyond carving it in "stone" weights.