ICML 2026 Papers

Learning with shared representation is widely recognized as an effective way to separate commonalities from heterogeneity across various heterogeneous sources. Most existing work includes all related data sources via simultaneously training a common feature extractor and source-specific heads. It is well understood that data sources with low relevance or poor quality may hinder representation learning. In this paper, we further dive into the question of which data sources should be learned jointly by focusing on the traditionally deemed "good" collection of sources, in which individual sources have similar relevance and qualities with respect to the true underlying common structure. Towards tractability, we focus on the linear setting where sources share a low-dimensional subspace. We find that source screening can play a central role in statistically optimal subspace estimation. We show that, for a broad class of problem instances, training on a carefully selected subset of sources suffices to achieve minimax optimality, even when a substantial portion of data is discarded. We formalize the notion of an informative subpopulation, develop algorithms and practical heuristics for identifying such subsets, and validate their effectiveness through both theoretical analysis and empirical evaluations on synthetic and real-world datasets.

This work demonstrates how increasing the number of neurons in a network without increasing its total number of non-zero parameters improves performance. We show that this gain corresponds with a decrease in interference between multiple features that would otherwise share the same neurons. On symbolic Boolean tasks, splitting each neuron into sparser sub-neurons with knowledge of the clauses systematically reduces polysemanticity metrics and yields higher task accuracy. Notably, even random splits of neuron weights approximate these gains, indicating that reduced collisions, not precise assignment, are a primary driver. Consistent with the superposition hypothesis, the benefits of this framework grow with increasing interference: when polysemantic load is high, accuracy improvements are the largest. Transferring these insights to more realistic models, including classifiers over CLIP embeddings, convolutional neural networks, and deeper multilayer networks, we find that widening networks while maintaining a constant non-zero parameter count consistently increases accuracy. These results identify an interpretability-grounded mechanism to leverage width against superposition, improving performance without increasing the number of non-zero parameters. Such a direction is well matched to modern accelerators, where memory movement of non-zero parameters, rather than raw compute, is often a dominant bottleneck.

The adversarial robustness of attributions is a fundamental requirement for reliable explainability in deep learning, yet existing approaches typically rely on computationally expensive explicit regularization. In this work, we show that attribution robustness can arise implicitly from the learning dynamics of standard stochastic gradient descent. We theoretically motivate this effect through connections between parameter-space and input-space curvature, and validate it across architectures, datasets, and attribution methods, with negligible computational overhead. In contrast, we prove that such robustness gains often does not transfer to attention-based attribution under softmax normalization, due to inherent entropy constraints, and we validate this limitation experimentally. Finally, we show that replacing softmax attention with kernel-based attention restores the robustness gains in transformer models. Our results highlight learning dynamics as a principled and practical mechanism for robust explainability, and reveal fundamental limitations of attention-based attribution under normalization.

This paper studies a fundamental yet often overlooked premise in evolutionary multi-view classification (EMVC): the impact of label noise on EMVC, such as distorting fitness landscapes shaped by individual fitness values (e.g., test accuracy). Traditional EMVC assumes training labels are noise-free, yet this often fails in practice. As a result, label noise introduces harmful supervision during the training phase, resulting in distorted fitness landscapes and the emergence of fitness evaluation bias (FEB). This bias misguides the evolutionary trajectory, causing the search process to stagnate in local optima. Given that label noise largely stems from the mislabeling of samples near their decision boundaries by human annotators, we thus compared the decision boundaries of human annotators and models, and found discrepancies between the two. Based on this observation, we propose a simple yet effective ``detect-then-calibrate" data purification framework that leverages outlier analysis in the gradient space (i.e., treating outliers as noisy samples) and prototype calibration in the feature space (i.e., utilizing feature prototypes of noise-free samples to correct the labels of noisy samples). Experimental results demonstrate that this strategy can effectively purify the data and alleviate FEB; moreover, it can improve the performance of various multi-view learning paradigms in label noise scenarios. (https://github.com/LiShuailzn/ICML-2026-GFD-EMVC)

Active feature acquisition (AFA) is a sequential decision-making problem where the goal is to improve model performance for test instances by adaptively selecting which features to acquire. In practice, AFA methods often learn from retrospective data with systematic missingness in the features and limited task-specific labels. To address this limitation, we introduce Learning-to-Measure (L2M), which consists of i) reliable uncertainty quantification over unseen tasks, and ii) an uncertainty-guided feature acquisition agent that maximizes conditional mutual information. We demonstrate an autoregressive pre-training approach that underpins reliable uncertainty quantification and acquisition for tasks with arbitrary missingness. L2M operates directly on datasets with retrospective missingness and performs the task in-context, eliminating per-task retraining. Across synthetic and real-world tabular benchmarks, L2M matches or surpasses task-specific baselines, particularly under scarce labels and high missingness.

Despite their practical success, it remains unclear why Mixture of Experts (MoE) models can outperform dense networks beyond sheer parameter scaling. We study an iso-parameter regime where inputs exhibit latent modular structure but are corrupted by feature noise, a proxy for noisy internal activations. We show that sparse expert activation acts as a noise filter: compared to a dense estimator, MoEs achieve lower generalization error under feature noise, improved robustness to perturbations, and faster convergence speed. Empirical results on synthetic data and real-world language tasks corroborate the theoretical insights, demonstrating consistent robustness and efficiency gains from sparse modular computation.

Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still incomplete. In this work we investigate neural feature geometry through the lens of discrete geometry. Since the input data manifold is typically unobserved, we approximate it using geometric graphs that encode local similarity structure. We provide theoretical results on the evolution of these graphs during training, showing that nonlinear activations play a crucial role in shaping feature geometry in feedforward neural networks. Moreover, we discover that the geometric transformations resemble a discrete Ricci flow on these graphs, suggesting that neural feature geometry evolves analogous to Ricci flow. This connection is supported by experiments on over 20,000 feedforward neural networks trained on binary classification tasks across both synthetic and real-world datasets. We observe that the emergence of class separability corresponds to the emergence of community structure in the associated graph representations, which is known to relate to discrete Ricci flow dynamics. Building on these insights, we introduce a novel framework for locally evaluating geometric transformations through comparison with discrete Ricci flow dynamics. Our experimental results further suggest connections between the evolution of feature geometry, and training time and network depth.

We study feature bagging through the lens of algorithmic stability. Feature bagging is an ensemble strategy that aggregates base learners trained on randomly subsampled feature subsets, possibly in a data-dependent manner. We introduce feature instability (FI), the feature-axis analogue of instance instability (II), which measures sensitivity to removing a single feature. Smaller values of II or FI correspond to stronger stability, and our experiments show that FI captures generalization-relevant information complementary to II. Within this framework, we analyze feature bagging in both a parametric linear model and a model-free setting inspired by recursive feature subsampling in random forests. In both settings, we establish formal guarantees showing that feature bagging improves the relevant stability relative to its non-bagged counterpart, with larger improvements under more aggressive subsampling. We further show that a modest number of bagging rounds is sufficient to approach the infinite-bagging stability level.

Mechanistic interpretability reveals that safety-critical behaviors (e.g., alignment, jailbreak, backdoor) in Large Language Models (LLMs) are grounded in specialized functional components. However, existing safety attribution methods struggle with generalization and reliability due to their reliance on heuristic, domain-specific metrics and search algorithms. To address this, we propose SafeSeek, a unified safety interpretability framework that identifies functionally complete safety circuits in LLMs via optimization. Unlike methods focusing on isolated heads or neurons, SafeSeek introduces differentiable binary masks to extract multi-granular circuits through gradient descent on safety datasets, while integrates Safety Circuit Tuning to utilize these sparse circuits for efficient safety fine-tuning. We validate SafeSeek in two key scenarios in LLM safety: \textbf{(1) backdoor attacks}, identifying a backdoor circuit with 0.42\% sparsity, whose ablation eradicates the Attack Success Rate (ASR) from 100\% $\to$ 0.4\% while retaining over 99\% general utility; \textbf{(2) safety alignment}, localizing an alignment circuit with 3.03\% heads and 0.79\% neurons, whose removal spikes ASR from 0.8\% $\to$ 96.9\%, whereas excluding this circuit during helpfulness fine-tuning maintains 96.5\% safety retention.

Sparse Autoencoders (SAEs) are widely used to interpret large language models by decomposing activations into sparse, human-understandable features, but scaling to large dictionaries exposes fundamental challenges. Systematic studies reveal pervasive feature splitting that fragments coherent concepts into non-atomic latents and widespread feature absorption that creates arbitrary exceptions in general features, severely compromising latent reliability. These issues stem from inconsistent latent assignment across samples: without cross-sample constraints, per-sample optimization often allows a single underlying concept to be inconsistently distributed across multiple redundant or interfering latents. To address this, we introduce C$^2$R (\underline{\textbf{C}}ross-sample \underline{\textbf{C}}onsistency \underline{\textbf{R}}egularization). C$^2$R explicitly encourages that each semantic feature is consistently represented by a unified latent across the batch by penalizing the co-activation of directionally similar latents. Comprehensive evaluation demonstrates that C$^2$R effectively mitigates both splitting and absorption while, crucially, preserving reconstruction fidelity, providing a principled solution that enhances latent interpretability without degrading model performance. Source code is available\footnote{\url{https://github.com/hr-jin/Cross-sample-Consistency-Regularization}}.

Extracting causally meaningful features from time-series data is fundamental for robust machine learning under distribution shifts. In process monitoring, existing methods struggle to maintain detection performance when operating conditions change. Current approaches capture either temporal causal relationships or cross-environment invariance, but not both simultaneously. We propose Causal Feature Learning (CFL), a unified framework that jointly optimizes for temporal relevance and environment mean invariance. CFL formulates feature extraction as a generalized Rayleigh-quotient problem, maximizing correlation with target variables while penalizing sensitivity to environment-dependent mean shifts. Theoretical analysis establishes conditions under which CFL identifies a mean-invariant predictive subspace. Experiments on the Tennessee Eastman Process demonstrate that CFL achieves 93.69\% average fault detection rate, outperforming 15 baseline methods and validating the benefit of jointly capturing both aspects of causality.

Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2 regularization. We study the deep unconstrained feature model (UFM)—equivalent to a deep linear network with orthogonal inputs—trained without regularization, to isolate how gradient descent and depth alone shape NC. We show that depth induces an implicit low-rank bias: low-rank matrices propagate norm more efficiently through successive multiplications, promoting low-rank alternatives to NC. These alternatives, we argue, correspond to softmax codes: max-margin solutions previously found in width-bottlenecked networks. Analyzing training dynamics under spectral initialization, we identify an early-time repulsion among singular values that drives low-rank emergence, and characterize how depth shrinks NC's basin of attraction. Finally, we show that some effects act in the opposite direction: for randomly initialized networks, increasing width biases training toward higher-rank solutions. Our results provide the first asymptotic and dynamic characterization of implicit bias in deep UFMs trained with unregularized multiclass cross-entropy.

Low-dimensional structures appear ubiquitously in the eigenspectra of deep-learning matrices in classification networks trained in the overparameterized regime. While theoretical advances have aimed to explain this phenomenology, they typically succeed only in capturing subsets of the full behavior or rely on assumptions that cannot hold in practice. In this work, we provide an analytic explanation for the bulk–outlier structure of several canonical deep-learning matrices, including the Hessian, gradients, and weights. We achieve this using unconstrained feature models (UFMs), a now-common tool for studying the emergence of deep neural collapse (DNC). We show that DNC is the source of these low-dimensional eigenspectra: in each case, the eigenvalues and eigenvectors can be constructed from feature means, the characterizing objects of DNC. This provides a unifying analytic explanation for a wide range of spectral phenomena in deep learning and goes beyond empirical characterizations—which typically focus on eigenvalues—by providing a detailed analysis of eigenvectors. We prove that our results hold for both linear and ReLU networks and provide numerical validation in both the modeling context and standard deep-network architectures on canonical datasets.

We study how individual training examples shape the internal computation of looped transformers, where a shared block is applied for $\tau$ recurrent iterations to enable latent reasoning. Existing training-data influence estimators such as TracIn yield a single scalar score that aggregates over all loop iterations, obscuring when during the recurrent computation a training example matters. We introduce Step-Decomposed Influence (SDI), which decomposes TracIn into a length-$\tau$ influence trajectory by unrolling the recurrent computation graph and attributing influence to specific loop iterations. To make SDI practical at transformer scale, we propose a TensorSketch implementation that never materialises per-example gradients. Experiments on looped GPT-style models and algorithmic reasoning tasks show that SDI scales excellently, matches full-gradient baselines with low error and supports a broad range of data attribution and interpretability tasks with per-step insights into the latent reasoning process.

Graph class-incremental learning (GCIL) has emerged to address the challenge of learning from dynamically evolving graphs, which continuously learns new classes over a sequence of tasks while retaining performance on previously seen classes. However, existing GCIL methods assume a closed-set test distribution drawn only from seen tasks. This fundamentally contradicts real-world open-ended scenarios where future unknown classes inevitably emerge. Empirically, we observe that existing GCIL methods falter in such open-set settings due to severe representation drift and generalized overconfidence. To bridge this gap, we investigate the Open-Set GCIL problem and propose \textbf{SAFER} (\underline{S}ubspace-\underline{A}ware \underline{FE}ature \underline{R}eshaping), a novel framework that endows GCIL with intrinsic open-set capabilities under a replay-free constraint. Specifically, \textbf{SAFER} performs subspace-aware feature reshaping with drift-free fingerprints, unifying task routing and open-set rejection into a single energy-based metric. Furthermore, we introduce a geometric space-consistency regularization that explicitly improves intra-class compactness and suppresses cross-task representation drift. Extensive experiments on four benchmarks demonstrate that SAFER outperforms state-of-the-art baselines by margins of up to 5.2\% in accuracy and 31.3\% in open-set AUROC, all while maintaining near-zero forgetting under strict no-replay constraints.

While mechanistic interpretability has identified interpretable circuits in large language models (LLMs), their causal origins in training data remain elusive. We introduce *mechanistic data attribution* (MDA), a scalable framework that employs influence functions to trace interpretable units back to specific training samples. Through extensive experiments on the Pythia family, we causally validate that targeted intervention—removing or augmenting a small fraction of high-influence samples—significantly modulates the emergence of interpretable heads, whereas random interventions show no effect. Our analysis reveals that repetitive structural data (e.g., LaTeX, XML) acts as a mechanistic catalyst. Furthermore, we observe that interventions targeting induction head formation induce a concurrent change in the model’s in-context learning (ICL) capability. This provides direct causal evidence for the long-standing hypothesis regarding the functional link between induction heads and ICL. Finally, we propose a mechanistic data augmentation pipeline that consistently accelerates circuit convergence across model scales, providing a principled methodology for steering the developmental trajectories of LLMs.

Real-time estimation of average treatment effects (ATE) in streaming observational data poses two key challenges: strict memory constraints that preclude storing the full data history, and distributional shifts in both treatment assignment and outcome-generating process. Existing methods either require offline access to the entire dataset for covariate balancing or rely on parametric online models that are vulnerable to model misspecification under such shifts. This paper proposes a novel model-agnostic method for ATE estimation in streaming data, which effectively addresses the above challenges. Based on discrepancy theory, we first compress streaming data into feature coresets that preserve covariate balancing objectives over a rich nonparametric function class, enabling linear-time updates with bounded memory. Then, by directly learning balancing weights and bypassing parametric propensity score estimation, we enhance the model's robustness against the shift in treatment assignment, while by balancing over an expressive function space we make the model more adaptive to the shift in the outcome-generating process. Theoretically, we establish convergence guarantees with explicit bounds on memory usage and computational complexity. Empirically, extensive experiments on both synthetic and real-world datasets show the effectiveness and robustness of the proposed method, consistently outperforming existing techniques.

The maximal coding rate reduction ($\text{MCR}^2$) objective is proposed for learning low-dimensional subspace representations and for principled deep model design, where layer structures are derived by unrolling its optimization steps. However, existing methods motivated by this objective do not fully adhere to design principles implied by the $\text{MCR}^2$ gradient, which weakens the principled and interpretable foundations of the resulting models. In this work, we introduce PACEAttention, a novel principled attention mechanism inspired by the *geometric insight* of $\text{MCR}^2$, whose gradient-based updates move features along directions shaped by the underlying low-dimensional feature structure. Our method captures this structure by leveraging randomization to guide feature updates. This principled construction enables the resulting PACENet to exhibit enhanced interpretability, with different heads attending to distinct image regions and capturing *fine-grained* structures under simple supervised training. Experiments demonstrate that PACEAttention achieves superior performance and more stable scalability than previous principled modules while remaining low complexity.

Large language models (LLMs) are highly sensitive to even small amounts of unsafe training data, making effective detection and filtering essential for trustworthy model development. Current state-of-the-art (SOTA) detection approaches primarily rely on moderation classifiers, which require significant computation overhead for training and are limited to predefined taxonomies. In this work, we explore data attribution approaches that measure the similarity between individual training samples and a small set of unsafe target examples, based on data representations such as hidden states or gradients. We identify a key limitation in existing methods: unsafe target texts contain both critical tokens that make them unsafe and neutral tokens (e.g., stop words or benign facts) that are necessary to form fluent language, and the latter of which makes the overall representations noisy for the purpose of detecting unsafe training data. To address this challenge, we propose Denoised Representation Attribution (DRA), a novel representation-based data attribution approach that denoises training and target representations for unsafe data detection. Across tasks of filtering jailbreaks and detecting gender bias, the proposed approach leads to significant improvement for data attribution methods, outperforming SOTA methods that are mostly based on moderation classifiers.