ICLR 2026 论文列表

Fairness in machine learning has emerged as a central concern, as predictive models frequently inherit or even amplify biases present in training data. Such biases often manifest as unintended correlations between model outcomes and sensitive attributes, leading to systematic disparities across demographic groups. Existing approaches to fair learning largely fall into two directions: incorporating fairness constraints tailored to specific definitions, which limits their generalizability, or reducing the statistical dependence between predictions and sensitive attributes, which is more flexible but highly sensitive to the choice of distance measure. The latter strategy in particular raises the challenge of finding a principled and reliable measure of dependence that can perform consistently across tasks. In this work, we present a general and model-agnostic approach to address this challenge. The method is based on encouraging independence between predictions and sensitive features through an optimization framework that leverages the Cauchy–Schwarz (CS) Divergence as a principled measure of dependence. Prior studies suggest that CS Divergence provides a tighter theoretical bound compared to alternative distance measures used in earlier fairness methods, offering a stronger foundation for fairness-oriented optimization. Our framework, therefore, unifies prior efforts under a simple yet effective principle and highlights the value of carefully chosen statistical measures in fair learning. Through extensive empirical evaluation on four tabular datasets and one image dataset, we show that our approach consistently improves multiple fairness metrics while maintaining competitive accuracy.

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work has focused mainly on estimating the Lipschitz constant of multi-layer perceptrons and convolutional neural networks. Here we focus on data modeled as sets or multisets of vectors and on neural networks that can handle such data. These models typically apply some permutation invariant aggregation function, such as the sum, mean or max operator, to the input multisets to produce a single vector for each input sample. In this paper, we investigate whether these aggregation functions, along with an attention-based aggregation function, are Lipschitz continuous with respect to three distance functions for unordered multisets, and we compute their Lipschitz constants. In the general case, we find that each aggregation function is Lipschitz continuous with respect to only one of the three distance functions, while the attention-based function is not Lipschitz continuous with respect to any of them. Then, we build on these results to derive upper bounds on the Lipschitz constant of neural networks that can process multisets of vectors, while we also study their stability to perturbations and generalization under distribution shifts. To empirically verify our theoretical analysis, we conduct a series of experiments on datasets from different domains.

Central to the widespread use of t-distributed stochastic neighbor embedding (t-SNE) is the conviction that it produces visualizations whose structure roughly matches that of the input. To the contrary, we prove that (1) the strength of the input clustering, and (2) the extremity of outlier points, cannot be reliably inferred from the t-SNE output. We demonstrate the prevalence of these failure modes in practice as well.

Autoencoders are widely used for dimensionality reduction, based on the assumption that high-dimensional data lies on low-dimensional manifolds. Regularized autoencoders aim to preserve manifold geometry during dimensionality reduction, but existing approaches often suffer from non-injective mappings and overly rigid constraints that limit their effectiveness and robustness. In this work, we identify encoder non-injectivity as a core bottleneck that leads to poor convergence and distorted latent representations. To ensure robustness across data distributions, we formalize the concept of admissible regularization and provide sufficient conditions for its satisfaction. In this work, we propose the Bi-Lipschitz Autoencoder (BLAE), which introduces two key innovations: (1) an injective regularization scheme based on a separation criterion to eliminate pathological local minima, and (2) a bi-Lipschitz relaxation that preserves geometry and exhibits robustness to data distribution drift. Empirical results on diverse datasets show that BLAE consistently outperforms existing methods in preserving manifold structure while remaining resilient to sampling sparsity and distribution shifts.

Recent optimizers like Muon, Scion, and Gluon have pushed the frontier of large-scale deep learning by exploiting layer-wise linear minimization oracles (LMOs) over non-Euclidean norm balls, capturing neural network structure in ways traditional algorithms cannot. Yet, no principled distributed framework exists for these methods, and communication bottlenecks remain unaddressed. The very few distributed variants are heuristic, with no convergence guarantees in sight. We introduce EF21-Muon, the first communication-efficient, non-Euclidean LMO-based optimizer with rigorous convergence guarantees. EF21-Muon supports stochastic gradients, momentum, and bidirectional compression with error feedback–marking the first extension of error feedback beyond the Euclidean setting. It recovers Muon/Scion when compression is off and specific norms are chosen, providing the first efficient distributed implementation of this powerful family. Our theory covers non-Euclidean smooth and the more general (L0, L1)–smooth setting, matching best-known Euclidean rates and enabling faster convergence under suitable norm choices. We further extend the analysis to layer-wise (generalized) smoothness regimes, capturing the anisotropic structure of deep networks. Experiments on NanoGPT benchmarking EF21-Muon against uncompressed Muon/Scion/Gluon demonstrate up to 7× communication savings with no accuracy degradation.

We show that a language model’s ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that representation dispersion—the average pairwise cosine distance among hidden vectors—strongly and negatively correlates with perplexity across diverse model families (LLaMA, Qwen, and others) and domains (Wikipedia, news, scientific abstracts). Beyond illustrating this link, we show how dispersion can be leveraged for a range of practical tasks—without requiring labeled data. First, measuring dispersion on unlabeled text allows us to predict downstream accuracy in new domains, offering a data‐efficient tool for model selection. Next, we find that identifying layers with higher dispersion pinpoints the best representations for retrieval‐based methods such as kNN‐LM, bypassing exhaustive layer‐by‐layer searches. Finally, we integrate a simple “push‐away” objective into training, which increases dispersion in both single‐domain and cross‐domain scenarios and directly improves perplexity in each.

Pre-training world models on large, action-free video datasets offers a promising path toward generalist agents, but a fundamental flaw undermines this paradigm. Prevailing methods train models to predict a single, deterministic future, an objective that is ill-posed for inherently stochastic environments where actions are unknown. We contend that a world model should instead learn a structured, probabilistic representation of the future where predictive uncertainty correctly scales with the temporal horizon. To achieve this, we introduce a pre-training framework, **H**orizon-c**A**librated **U**ncertainty **W**orld **M**odel (HAUWM), built on a probabilistic ensemble that predicts frames at randomly sampled future horizons. The core of our method is a Horizon-Calibrated Uncertainty (HCU) loss, which explicitly shapes the latent space by encouraging predictive variance to grow as the model projects further into the future. This approach yields a latent dynamics model that is not only predictive but also equipped with a reliable measure of temporal confidence. When fine-tuned for downstream control, our pre-trained model significantly outperforms state-of-the-art methods across a diverse suite of benchmarks, including MetaWorld, the DeepMind Control Suite, and RoboDesk. These results highlight the critical role of structured uncertainty in robust decision-making.

We propose a simple yet novel data augmentation method for general data modalities based on energy-based modeling and principles from information geometry. Unlike most existing learning-based data augmentation methods, which rely on learning latent representations with generative models, our proposed framework enables an intuitive construction of a geometrically aware latent space that represents the structure of the data itself, supporting efficient and explicit encoding and decoding procedures. We then present and discuss how to design latent spaces that will subsequently control the augmentation with the proposed algorithm. Empirical results demonstrate that our data augmentation method achieves competitive performance in downstream tasks compared to other baselines, while offering fine-grained controllability that is lacking in the existing literature.

ViTs are general and accurate, and address many tasks, but ViTs are slow, and are not always practical when efficiency is key. Existing methods for faster ViTs design hybrid non-ViT architectures, losing generality, or shrink their tokens, sacrificing accuracy. While many non-ViT architectures are both fast and accurate, they cannot flexibly process other input shapes, pre-train by SOTA self-supervised learning, reduce computation by dropping tokens, and more like ViTs can. We make ViTs faster by reducing patch token width while increasing global token width by adding a new Jumbo token. Our wider Jumbo token is processed by its own wider FFN to increase model capacity. Yet our Jumbo FFN is efficient: it processes a single token, for speed, and its parameters are shared across all layers, for memory. Crucially, our Jumbo is attention-only and non-hierarchical, like a plain ViT, so it is simple, scalable, flexible, and compatible with ViT methods new and old. Jumbo improves over ViT baselines with Registers from Nano to Large scales while maintaining speed/throughput on ImageNet-1K (↑0.1−13%). Jumbo also improves MAE pre-training (↑4.9% linear probing on ImageNet-1K), test-time adaptation (↑5.2% on ImageNet-C), and time series modeling. Our Jumbo models even achieve better speed-accuracy trade-offs than specialized non-ViT compute-efficient models, while maintaining plain-ViT compatibility for practicality.

Event cameras deliver visual data with high temporal resolution, low latency, and minimal redundancy, yet their asynchronous, sparse sequential nature challenges standard tensor-based machine learning (ML). While the recent asynchronous-to-synchronous (A2S) paradigm aims to bridge this gap by asynchronously encoding events into learned features for ML pipelines, existing A2S approaches often sacrifice expressivity and generalizability compared to dense, synchronous methods. This paper introduces EVA (EVent Asynchronous feature learning), a novel A2S framework to generate highly expressive and generalizable event-by-event features. Inspired by the analogy between events and language, EVA uniquely adapts advances from language modeling in linear attention and self-supervised learning for its construction. In demonstration, EVA outperforms prior A2S methods on recognition tasks (DVS128-Gesture and N-Cars), and represents the first A2S framework to successfully master demanding detection tasks, achieving a 47.7 mAP on the Gen1 dataset. These results underscore EVA's potential for advancing real-time event-based vision applications.

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice, understanding the reason behind a model’s uncertainty and the type of uncertainty it represents can support risk-aware decisions, enhance user trust, and guide additional data collection. However, many existing methods only address a single type of uncertainty or require modifications and retraining of the base model, making them difficult to adopt in real-world systems. We introduce CUPID (Comprehensive Uncertainty Plug-in estImation moDel), a general-purpose module that jointly estimates aleatoric and epistemic uncertainty without modifying or retraining the base model. CUPID can be flexibly inserted into any layer of a pretrained network. It models aleatoric uncertainty through a learned Bayesian identity mapping and captures epistemic uncertainty by analyzing the model’s internal responses to structured perturbations. We evaluate CUPID across a range of tasks, including classification, regression, and out-of-distribution detection. The results show that it consistently delivers competitive performance while offering layer-wise insights into the origins of uncertainty. By making uncertainty estimation modular, interpretable, and model-agnostic, CUPID supports more transparent and trustworthy AI.

Current language models rely on static vocabularies determined at pretraining time, which can lead to decreased performance and increased computational cost for domains underrepresented in the original vocabulary. New tokens can be added to solve this problem, when coupled with a good initialization for their new embeddings. However, existing embedding initialization methods require expensive further training or pretraining of additional modules. In this paper, we propose Token Distillation and show that by distilling representations obtained using the original tokenization, we can quickly learn high-quality input embeddings for new tokens. Experimental results with a wide range of open-weight models show that Token Distillation outperforms even strong baselines.

Conventional supervised learning methods are often vulnerable to spurious correlations, particularly under distribution shifts in test data. To address this issue, several approaches, most notably Group DRO, have been developed. While these methods are highly robust to subpopulation or group shifts, they remain vulnerable to intra-group distributional shifts, which frequently occur in minority groups with limited samples. We propose a hierarchical extension of Group DRO that addresses both inter-group and intra-group uncertainties, providing robustness to distribution shifts at multiple levels. We also introduce new benchmark settings that simulate realistic minority group distribution shifts—an important yet previously underexplored challenge in spurious correlation research. Our method demonstrates strong robustness under these conditions—where existing robust learning methods consistently fail—while also achieving superior performance on standard benchmarks. These results highlight the importance of broadening the ambiguity set to better capture both inter-group and intra-group distributional uncertainties.

We study cross-domain lossy compression, where the encoder observes a degraded source while the decoder reconstructs samples from a distinct target distribution. The problem is formulated as constrained optimal transport with two constraints on compression rate and classification loss. With shared common randomness, the one-shot setting reduces to a deterministic transport plan, and we derive closed-form distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoffs for Bernoulli sources under Hamming distortion. In the asymptotic regime, we establish analytic DRC/RDC expressions for Gaussian models under mean-squared error. The framework is further extended to incorporate perception divergences (Kullback-Leibler and squared Wasserstein), yielding closed-form distortion-rate-perception-classification (DRPC) functions. To validate the theory, we develop deep end-to-end compression models for super-resolution (MNIST), denoising (SVHN, CIFAR-10, ImageNet, KODAK), and inpainting (SVHN) problems, demonstrating the consistency between the theoretical results and empirical performance.

We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over linear congruential generators (LCGs) by applying a series of bit-wise shifts, XORs, rotations and truncations to the hidden state. We show that Transformers can nevertheless successfully perform in-context prediction on unseen sequences from diverse PCG variants, in tasks that are beyond published classical attacks. In our experiments we scale moduli up to $2^{22}$ using up to $50$ million model parameters and datasets with up to $5$ billion tokens. Surprisingly, we find even when the output is truncated to a single bit, it can be reliably predicted by the model. When multiple distinct PRNGs are presented together during training, the model can jointly learn them, identifying structures from different permutations. We demonstrate a scaling law with modulus $m$: the number of in-context sequence elements required for near-perfect prediction grows as $\sqrt{m}$. For larger moduli, optimization enters extended stagnation phases; in our experiments, learning moduli $m \geq 2^{20}$ requires incorporating training data from smaller moduli, demonstrating a critical necessity for curriculum learning. Finally, we analyze embedding layers and uncover a novel clustering phenomenon: the top principal components spontaneously group the integers into bitwise rotationally-invariant clusters, revealing how representations can transfer from smaller to larger moduli.

In many real-world scenarios, precisely labeling graph data is costly or impractical, especially in domains like molecular biology or social networks, where annotation requires expert effort. This challenge motivates partial-label graph learning, where each graph is weakly annotated with a candidate label set containing the true label. However, such ambiguous supervision makes it hard to extract reliable semantics and increases the risk of overfitting to noisy candidates. To address these challenges, we propose PRISM, a unified framework that performs relational inference with spatial and spectral cues to resolve label ambiguity. PRISM captures discriminative spatial cues by aligning prototype-guided substructures across graphs and extracts global spectral cues by decomposing graph signals into multiple frequency bands with attention, preserving frequency-specific semantics. These complementary views are integrated into a hybrid relational graph, which supports confidence-aware label propagation under candidate constraints. A closed-loop refinement mechanism further stabilizes supervision via masked updates and momentum-based confidence estimation. Extensive experiments across diverse benchmarks demonstrate that PRISM consistently outperforms strong baselines under various noise settings, establishing a new paradigm for weakly supervised graph classification.

There has been significant recent interest on understanding the capacity of Transformers for in-context learning (ICL), yet most theory focuses on supervised settings with explicitly labeled pairs. In practice, Transformers often perform well even when labels are sparse or absent, suggesting crucial structure within unlabeled contextual demonstrations. We introduce and study in-context semi-supervised learning (IC-SSL), where a small set of labeled examples is accompanied by many unlabeled points, and show that Transformers can leverage the unlabeled context to learn a robust, context-dependent representation. This representation enables accurate predictions and markedly improves performance in low-label regimes, offering foundational insights into how Transformers exploit unlabeled context for representation learning within the ICL framework. Our code is available at https://github.com/Jason-fan20/ICL_Semi.

Axis-aligned decision trees are fast and stable but struggle on datasets with rotated or interaction-dependent decision boundaries, where informative splits require linear combinations of features rather than single-feature thresholds. Oblique forests address this with per-node hyperplane splits, but at added computational cost. We propose a simple alternative: JARF, Jacobian-Aligned Random Forests. Concretely, we fit a random forest to estimate class probabilities or regression outputs, compute finite-difference gradients with respect to each feature, form an expected Jacobian outer product/expected gradient outer product, and use it as a single global linear preconditioner for all inputs. This preserves the simplicity of axisaligned trees while applying a single global rotation to capture oblique boundaries and feature interactions that would otherwise require many axis-aligned splits to approximate. On tabular benchmarks, our preconditioned forest matches or surpasses oblique baselines while training faster. Our results suggest that supervised preconditioning can deliver the accuracy of oblique forests while keeping the simplicity of axis-aligned trees.

Despite multi-view clustering has achieved great progress in past decades, it is still a challenge to balance the effectiveness, efficiency, completeness and consistency of nonlinearly separable clustering for the data from different views. To address this challenge, we show that multi-view clustering can be regarded as a three-level optimization problem. To be specific, we divide the multi-view clustering into three sub-problems based on $ K $-means or kernel $ K $-means, i.e., linear clustering on the original multi-view dataset, nonlinear clustering on the set of obtained linear clusters and multi-view clustering by integrating partition matrices from different views obtained by linear and nonlinear clustering based on reconstruction. We propose Explainable $ K $-means Neural Networks (EKNN) and present how to unify these three sub-problems into a framework based on EKNN. It is able to simultaneously consider the effectiveness, efficiency, completeness and consistency for the nonlinearly multi-view clustering and can be optimized by an iterative algorithm. EKNN is explainable since the effect of each layer is known. To the best of our knowledge, this is the first attempt to balance the effectiveness, efficiency, completeness and consistency by dividing the multi-view clustering into three different sub-problems. Extensive experimental results demonstrate the effectiveness and efficiency of EKNN compared with other methods for multi-view clustering on different datasets in terms of different metrics.