ICML 2026 Papers

Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work, building on recent initiatives, we provide a unifying perspective by interpreting these seemingly disparate methods through the lens of Stochastic Frank-Wolfe. Specifically, we show that Lion and Muon with weight decay can be viewed as special instances of a Stochastic Frank-Wolfe, and we establish their convergence guarantees in terms of the Frank-Wolfe gap, a standard stationarity measure in non-convex optimization for Frank-Wolfe methods. We further find that convergence to this gap implies convergence to a KKT point of the original problem under a norm constraint for Lion and Muon. Moreover, motivated by recent empirical findings that stochastic gradients in modern machine learning tasks often exhibit heavy-tailed distributions, we extend Stochastic Frank-Wolfe to settings with heavy-tailed noise by developing two robust variants with strong theoretical guarantees that hold for general compact convex sets without the need for a large batch size, filling the gap in the literature on Stochastic Frank-Wolfe for non-convex optimization. Our contributions in the later part of this work, in turn, yield new variants of Lion and Muon, that better accommodate heavy-tailed gradient noise, thereby enhancing their practical scope.

This paper studies the AdamW-style Shampoo optimizer, an effective implementation of the classical Shampoo that notably won the external tuning track of the AlgoPerf neural network training algorithm competition. Our analysis unifies one-sided and two-sided preconditioning and establishes the convergence rate $\frac{1}{K}\sum_{k=1}^KE[|||\nabla f(X_k)|||]\leq O(\frac{\sqrt{m+n}C}{K^{1/4}})$ measured by nuclear norm (denoted as $|||\cdot|||$ to display correctly in OpenReview), where $K$ represents the iteration number, $(m,n)$ denotes the size of matrix parameters, and $C$ matches the constant in the optimal convergence rate of SGD. Theoretically, we have $||\nabla f(X)||\leq|||\nabla f(X)|||\leq\sqrt{\min(m,n)}||\nabla f(X)||$ (denote $||\cdot||$ as the Frobenius norm to display correctly in OpenReview), supporting that our convergence rate can be considered to be analogous to the optimal $\frac{1}{K}\sum_{k=1}^K E[||\nabla f(X_k)||]\leq O(\frac{C}{K^{1/4}})$ convergence rate of SGD in the ideal case of $|||\nabla f(X)|||= \Theta(\sqrt{\min(m,n)})||\nabla f(X)||$ and balanced $m$ and $n$.

Autoregressive Models (ARMs) have long dominated the landscape of Large Language Models. Recently, a new paradigm has emerged in the form of diffusion-based Large Language Models (dLLMs), which generate text by iteratively denoising masked segments. This approach has shown significant advantages and potential. However, dLLMs suffer from high inference latency. Traditional ARM acceleration techniques, such as Key-Value caching, are incompatible with dLLMs due to their bidirectional attention mechanism. To address this specific challenge, our work begins with a key observation that dLLM inference involves a static prompt and a partially dynamic response, where most tokens remain stable across adjacent denoising steps. Based on this, we propose dLLM-Cache, a training-free adaptive caching framework that combines long-interval prompt caching with partial response updates guided by feature similarity. This design enables efficient reuse of intermediate computations without compromising model performance. Extensive experiments on representative dLLMs, including LLaDA 8B and Dream 7B, show that dLLM-Cache achieves up to *9.1*$\times$ FLOPs reduction on LongBench-HotpotQA while maintaining competitive output quality. Notably, our method brings dLLM inference latency close to that of ARMs under many settings. *The code for this work is publicly available at: https://github.com/maomaocun/dLLM-cache*.

Large-scale medical biobanks provide imaging data complemented by extensive tabular information, such as clinical measurements or demographics. However, this abundance of tabular attributes does not reflect real-world datasets, where only a subset of attributes may be available. This discrepancy calls for methods that remain robust to missing values at inference. To address this challenge, we propose RoVTL (Robust Vision-Tabular Learning), a framework designed to handle any level of tabular data availability, from 0% to 100%. RoVTL comprises two key stages: contrastive pretraining, where we introduce tabular attribute missingness as data augmentation to promote robustness, and downstream task tuning, where tabular missingness is complemented by a novel Tabular More vs. Fewer loss that ranks performance based on the amount of available tabular data. Combined with gated-cross attention fusion module, our tuning approach enables consistent performance across all tabular data completeness scenarios. We evaluate RoVTL on cardiac MRI scans from the UK Biobank, demonstrating superior robustness to missing tabular data compared to prior methods. Furthermore, RoVTL successfully generalizes to an external cardiac MRI dataset for multimodal disease classification, and extends to the natural images domain, achieving robust performance on a car advertisements dataset. The model weights and code are available at https://github.com/marteczkah/RoVTL.

Recent advances in autoregressive video diffusion have enabled real-time frame streaming, however, existing methods still suffer from visual error accumulation including visual fidelity and motion degradation over long-horizon. To address these challenges, we introduce Deep Forcing, a training-free extension of autoregressive video diffusion models that stabilizes long video generation through two complementary mechanisms. Deep Sink preserves approximately half of the sliding context window as persistent sink tokens and realigns their temporal RoPE phases to the current timeline, thereby maintaining global context during extended rollouts. Participative Compression performs importance-aware KV cache pruning, retaining only tokens that actively participate in recent attention while removing redundant or degraded history, effectively mitigating error accumulation under out-of-distribution lengths. Together, these components enable over 12× length extrapolation (e.g., 5s-trained → 60s+) without sacrificing inference speed, while improving visual fidelity and motion dynamics compared to prior methods. Our results demonstrate that Deep Forcing can achieve performance comparable to state-of-the-art training-based methods trained specifically for long video generation.

Foundation models show great promise in achieving zero-shot or few-shot forecasting for ODE-based chaotic systems via large-scale pretraining. However, existing architectures often fail to capture the multi-scale temporal structures and distinct spectral characteristics of chaotic dynamics. To address this, we introduce ChaosNexus, a foundation model for chaotic system forecasting underpinned by the proposed ScaleFormer architecture. By processing temporal contexts across hierarchically varying patch sizes, ChaosNexus effectively captures long-range dependencies and preserves high-frequency fluctuations. To address heterogeneity across distinct systems, we integrate Mixture-of-Experts (MoE) layers into each ScaleFormer block and explicitly condition the final forecasts on a learned frequency fingerprint, providing the model with a global spectral view of the system. Extensive evaluations on over 9,000 synthetic systems demonstrate that ChaosNexus achieves superior fidelity in long-term attractor statistics while maintaining competitive point-wise accuracy. Furthermore, in real-world applications, it achieves a remarkable zero-shot mean error below 1°C for 5-day station-based weather forecasting. Code is available at https://github.com/tsinghua-fib-lab/ChaosNexus.

Diffusion-based large language models generate text by gradually filling in masked tokens, yet they remain slow because they usually decode only a few tokens per step. Parallel decoding, which unmasks multiple tokens simultaneously, promises acceleration but often degrades quality when too many tokens are predicted at once. We identify the root cause: when decoding is viewed as iterative token grouping, overly permissive grouping places interdependent tokens in the same step, violates the conditional independence assumption, and amplifies reliance on noisy context even when the top prediction is already correct. We introduce SPEED, a framework that enlarges safe parallel groups through complementary training and inference designs. At training time, a sharpened teacher distillation objective selectively aligns the student to teacher-correct positions using a temperature-scaled KL term together with a masked language modeling loss, producing a student that assigns more probability mass to correct token identities and elevates more positions above the decoding threshold. At inference time, Slow-Fast Decoding partitions tokens by sensitivity to revealed context using token-wise Jensen-Shannon Divergence computed with and without access to the preceding block, decoding low-sensitivity tokens jointly in parallel while deferring high-sensitivity tokens until sufficient context resolves them. Through extensive experiments, our framework attains up to 12.2$\times$ speedup on LLaDA-8B-Instruct and 6.7$\times$ on Dream-7B-Instruct with accuracy close to greedy decoding across standard reasoning and code benchmarks.

Despite the remarkable success of Vision Transformers (ViTs) across a wide range of vision tasks, recent studies have revealed that they remain vulnerable to adversarial examples, much like Convolutional Neural Networks (CNNs). A common empirical defense strategy is adversarial training, yet the theoretical underpinnings of its robustness in ViTs remain largely unexplored. In this work, we present the first theoretical analysis of adversarial training under simplified ViT architectures. We show that, when trained under a signal-to-noise ratio that satisfies a certain condition and within a moderate perturbation budget, adversarial training enables ViTs to achieve nearly zero robust training loss and robust generalization error under certain regimes. Remarkably, this leads to strong generalization even in the presence of overfitting, a phenomenon known as benign overfitting, previously only observed in CNNs (with adversarial training). Experiments on both synthetic and real-world datasets further validate our theoretical findings.

In many applications, practical constraints prevent measuring covariates and outcomes on the same units, resulting in unpaired data. We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates $X$ and an outcome $Y$ under different experimental conditions (environments) but do not observe them jointly -- we either observe $X$ or $Y$. Under appropriate regularity conditions, the problem can be cast as an instrumental variable (IV) regression with the environment acting as a (possibly high-dimensional) instrument. When there are many environments but only a few observations per environment, standard two-sample IV estimators fail to be consistent. We propose a GMM-type estimator based on cross-fold sample splitting of the instrument–covariate sample that also applies in standard IV settings. We prove that it is consistent as the number of environments grows but the sample size per environment remains constant. We further extend the method to sparse causal effects via $\ell_1$-regularized estimation and post-selection refitting.

Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from lookahead heuristics such as strong branching, and linear programming (LP) bound improvement for cut selection. Training and evaluation of the learned models often focus on local score accuracy. We show that such local score-based methods can lead to search trees exponentially larger than optimal tree sizes, by identifying two sources of this gap. The first is that these widely used expert signals can be misaligned with overall tree size. LP bound improvement can select a root cut set that yields an exponentially larger strong branching tree than selecting cuts by a simple proxy score, and strong branching itself can be exponentially suboptimal (Dey et al., 2024). The second is that small discrepancies can be amplified by the branch-and-bound recursion. An arbitrarily small perturbation of the right-hand sides in a root cut set can change the minimum tree size from a single node to exponentially many. For branching, arbitrarily small score discrepancies, and differences only in tie-breaking, can produce trees of exponentially different sizes, and even a small number of decision differences along a trajectory can incur exponential growth. These results show that branch-and-cut policies trained and learned using local expert scores do not guarantee small trees, thus motivating the study of data-driven methods that produce policies better aligned with tree size rather than only accuracy on expert scores.

One-step diffusion models have demonstrated a promising capability and fast inference in video super-resolution (VSR) for real-world applications. Nevertheless, the substantial model size and high computational cost of Diffusion Transformers (DiTs) limit downstream applications. While low-bit quantization is a common approach for model compression, the effectiveness of quantized models is challenged by the high dynamic range of input latent and diverse layer behaviors. To address these challenges, we introduce LSGQuant, a layer-sensitivity-guided quantization approach for one-step diffusion-based real-world VSR. Our method incorporates a Dynamic Range Adaptive Quantizer (DRAQ) to fit video token activations. Furthermore, we estimate layer sensitivity and implement a Variance-Oriented Layer Training Strategy (VOLTS) by analyzing layer-wise statistics in calibration. We also introduce Quantization-Aware Optimization (QAO) to jointly refine the quantized branch and a retained high-precision branch. Extensive experiments demonstrate that our method has nearly the performance of the original model with full-precision and significantly exceeds existing quantization techniques. All models and code are available at https://github.com/zhengchen1999/LSGQuant.

Spiking Neural Networks (SNNs) can achieve competitive performance by converting already existing well-trained Artificial Neural Networks (ANNs), avoiding further costly training. This property is particularly attractive in Reinforcement Learning (RL), where training through environment interaction is expensive and potentially unsafe. However, existing conversion methods perform poorly in continuous control, where suitable baselines are largely absent. We identify error amplification as the key cause: small action approximation errors become temporally correlated across decision steps, inducing cumulative state distribution shift and severe performance degradation. To address this issue, we propose Cross-Step Residual Potential Initialization (CRPI), a lightweight gradient-free mechanism that carries over residual membrane potentials across decision steps to suppress temporally correlated errors. Experiments on continuous control benchmarks with both vector and visual observations demonstrate that CRPI can be integrated into existing conversion pipelines and substantially recovers lost performance. Our results highlight continuous control as a critical and challenging benchmark for ANN-to-SNN conversion, where small errors can be strongly amplified and impact performance. Code is available at https://github.com/xuzijie32/ANN2SNN-CRPI.

Large Language Model (LLM)-based agents employ external and internal memory systems to handle complex, goal-oriented tasks, yet this exposes them to severe extraction attacks, and corresponding defenses are currently lacking. In this paper, we propose *MemPot*, the first theoretically verified defense framework against memory extraction attacks by injecting optimized honeypots into the memory. Through a two-stage optimization process, *MemPot* generates trap documents that maximize the retrieval probability for attackers while remaining inconspicuous to benign users. We model the detection process as Wald’s Sequential Probability Ratio Test (SPRT) and theoretically prove that *MemPot* achieves a lower average number of sampling rounds compared to optimal static detectors. Empirically, *MemPot* significantly outperforms state-of-the-art baselines, achieving a 50% improvement in detection AUROC and an 80% increase in True Positive Rate under low False Positive Rate constraints. Furthermore, our experiments confirm that *MemPot* incurs zero online inference latency and preserves the agent's utility on standard tasks, verifying its superiority in safety, harmlessness and efficiency.

Protein-protein interactions (PPIs) are essential for many biological processes. However, existing PPI prediction approaches suffer from two major limitations: they overlook the hierarchical organization of proteins, particularly meso-scale motifs that critically regulate PPIs, and fail to effectively integrate sequence, structure, and function modalities. To address these limitations, we propose MMM-PPI, a Hierarchical Motif-based Multi-Modal protein Encoder for PPI Prediction that constructs PPI embeddings in a bottom-up multi-modal manner across three scales. At the micro-scale, we encode three modal residue features; at the meso-scale, a novel multimodal motif encoder aggregates residues into spatially-informed motif embeddings; at the macro-scale, a multimodal protein encoder integrates motifs into protein embeddings by jointly modeling motif importance and inter-modal correlations. The pre-trained encoder can be used off-the-shelf for large-scale PPI prediction. Extensive experiments on multiple PPI datasets show that MMM-PPI outperforms state-of-the-art multi-label PPI prediction models, particularly under challenging data partitions and limited data scenarios. Codes are in https://github.com/yzf-code/MMM-PPI.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of $M \ge 3$ models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.

Geometry-aware generative models and novel view synthesis approaches have shown strong potential in visual fidelity and consistency. In parallel, equivariant representation learning has emerged as a powerful framework for constructing latent spaces where analytically known group transformations could act directly, capturing geometric structure in data and enhancing both interpretability and generalization in novel view synthesis. However, we identify that existing approaches often suffer from latent misalignment, a discrepancy between the intended group action and the actually required transformations in the latent space. Consequently, the learned latents often fail to consistently preserve the equivariant relations imposed by the underlying group symmetry. To address this, we propose Residual Latent Flow, a flow-based framework that corrects the misaligned latents, thereby improving compliance with the underlying equivariance relation. Our comprehensive experiments show that our method significantly reduces latent misalignment and improves novel view synthesis quality, under rotation groups SO(n).

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine satisfiability. We introduce a diagnostic benchmark for 2-SAT built from parameterized families of structured 2-CNF formulas, where satisfiability is characterized by the implication graph and can be tuned along interpretable axes. Our generators isolate distinct competencies and failure modes: (i) contradiction-cycle UNSAT cores with controllable size and imbalance, (ii) SAT instances with a prescribed fraction of free variables to control solution multiplicity, (iii) planted backbones that modulate propagation, (iv) late bridge clauses that couple otherwise monotone regions to probe sensitivity to ordering and revision, and (v) symmetry/duplication variants that test abstraction under renaming and redundant structure. We evaluate LLM-based reasoners on decision accuracy and assignment validity, and quantify robustness under semantics-preserving perturbations such as clause reordering, filler clauses, and variable renaming. Across models, we observe sharp performance transitions under targeted structural interventions even when surface statistics are held fixed, revealing brittleness regimes that are invisible to aggregate SAT accuracy.

In safety-critical domains where online data collection is infeasible, offline reinforcement learning (RL) is attractive only if policies achieve high returns without catastrophic lower-tail risk. Prior work on risk-averse offline RL achieves safety at the cost of value- or model-based pessimism, and restricted policy classes that limit policy expressiveness, whereas diffusion/flow-based expressive generative policies have largely been used in risk-neutral settings. We introduce **Risk-Aware Multimodal Actor-Critic (RAMAC)**, a simple, modular, model-free framework that couples an expressive generative actor (e.g., diffusion/flow) with a distributional critic and optimizes a composite objective that combines Conditional Value-at-Risk (CVaR) with behavioral cloning (BC), enabling risk-sensitive learning in complex multimodal scenarios. Since out-of-distribution (OOD) actions are a major driver of catastrophic failures in offline RL, we further provide an objective-level analysis showing that controlling behavior divergence via BC suppresses OOD actions and stabilizes CVaR. Instantiating RAMAC with a diffusion actor, we illustrate these insights on a 2-D risky bandit and evaluate on Stochastic-D4RL, observing consistent gains in CVaR$_{0.1}$ while maintaining strong returns.