ICML 2026 论文列表

In this paper, we present the convergence analysis of the proximal Alternating Direction Method of Multipliers (ADMM) for problems with block anti-upper triangular constraints. While the linear constraints can be treated separately, most analyses of ADMM and its variants predominantly regard the linear constraints as one. Hence, it relies on assumptions related to the entire constraint matrix, such as the full column rank. However, some problems with block anti-upper triangular constraints that can be solved by ADMM do not satisfy these assumptions. To fill this gap, a new assumption is proposed and used to guarantee the global convergence of the proximal ADMM for nonconvex problems. In the strongly convex setting, we also prove the global convergence of the proximal ADMM and establish the linear convergence under four different scenarios. This work extends the theoretical understanding of the multi-block ADMM to more general cases with block anti-upper triangular constraints.

Scientific embodied agents could automate laboratory workflows, but laboratory success is trajectory-level: an agent must remain safe throughout execution, not merely reach a final goal. In benchtop settings a small pose, force, or tilt error can cause irreversible spillage or equipment damage, yet most robot benchmarks evaluate reversible, high-tolerance manipulation and imitation-trained policies receive no recovery signal for execution drift. We introduce SafeLab, a generative simulation benchmark that couples a verified generative engine, an automated expert for teleoperation-free demonstrations, and a safety-aware RL interface, with 63 calibrated laboratory assets, 64 tasks across 9 manipulation categories, and 6,400 expert trajectories. Across state-of-the-art policies, it reveals unsafe-but-successful trajectories—large gaps between task success and Safe Success Rate—most acutely in liquid handling, force-limited actuation, and bimanual glassware rearrangement. Bounded residual RL then learns execution-level corrections that raise the simulated Safe Success Rate by up to 43.0 percentage points without retraining the base policy. Finally, 50 open-loop physical replays show 86% agreement between simulated and observed safety outcomes, supporting SafeLab as a scalable platform for screening and training safer laboratory agents.

Learning permutation-invariant functions over sets of $N$ elements, where the output is independent of the input ordering, is fundamental to many deep learning applications. While sum-decomposable architectures like DeepSets offer universal approximation for such functions, existing constructive bounds require a latent dimension of $\mathcal{O}(N)$, posing a significant scalability bottleneck. We break this barrier for *Wasserstein-stable* functions, i.e., those that are Lipschitz continuous with respect to the Wasserstein-1 metric on input distributions. We constructively prove that a latent dimension of $\mathcal{O}\left(C_D\varepsilon^{-(3D+4)}\log(N+\varepsilon^{-D})\right)$ suffices for uniform approximation as $ \varepsilon\to 0 $, where $D$ is the element dimension and $C_D$ is a constant depending only on $D$. We first discretize the input space into a finite net of measures with covering number polynomial in $N$. We then embed it via a multiscale Random Fourier Feature encoder that guarantees both Lipschitz stability and Hölder separation. Finally, we recover the target function via a McShane-extended Hölder decoder. This result advances the theoretical understanding of the expressivity and scalability of set-based neural architectures.

Large Language Models (LLMs) have intensified the need for low-precision formats for efficient inference. The Open Compute Project Microscaling (MX) standard is attractive due to its favorable hardware efficiency, but its 4-bit variant (MXFP4) lags behind NVIDIA’s NVFP4 in accuracy, limiting adoption. We introduce two software-only techniques, Overflow-Aware Scaling (OAS) and Macro Block Scaling (MBS), that improve MXFP4 quantization fidelity without requiring hardware changes. OAS reduces overall errors by increasing effective dynamic range under power-of-two block scaling, while MBS allocates higher-precision scaling at a coarser granularity to better preserve outliers. Across multiple LLMs and standard downstream benchmarks, OAS and MBS reduce the end-to-end accuracy gap between MXFP4 and NVFP4 from about 10% to below 1% on average, while incurring modest GEMM overhead (6.2% on average). These results re-establish MXFP4 as a practical alternative to NVFP4, enabling near-NVFP4 accuracy while retaining MX’s hardware-efficiency advantages (e.g., 12% relative area savings in tensor cores).

Phenotypic screening experiments produce many microscope images of cells under diverse perturbations, with biologically significant responses often subtle or difficult to identify visually. A central challenge is to extract image representations that distinguish activity from controls and group phenotypically similar perturbations. In this work we propose new adaptations of contrastive loss functions that incorporate experimental metadata as learned class vectors, and a geometrically inspired variant, called SPC, where class vectors are confined to the unit sphere and updated only by attractive terms (allowing more overlap of phenotypically similar classes). The approach is tested on two popular benchmarking datasets, BBBC021 and RxRx3-core; and we also evaluate performance on uncurated screens of HaCaT cells to gauge effectiveness in a realistic use-case scenario. We find we outperform prior methods across the three datasets and on a wide array of metrics measuring phenotype grouping, biological recall, drug-target interaction and mechanism-of-action inference. We also show we maintain this improved performance compared to models over 10x larger in parameter count, and that SPC can be used as an effective fine-tuning technique. The method is easy to implement and is well suited to settings with limited data or compute resources.

Outdoor LiDAR generation has shown strong potential for autonomous driving and large-scale 3D perception. However, existing approaches remain computationally intensive and primarily static, lacking explicit modeling of temporal dynamics. This limitation weakens spatiotemporal coherence and reduces the realism of 4D LiDAR generation. We propose a hierarchical recoupling generation framework that explicitly disentangles and reconstructs large-scale geometry and motion within a unified hierarchical structure. First, we design a multi-resolution feature scaffold that predicts time-correlated unsigned distance fields and spatial gradients, enabling hierarchical decomposition of 4D dynamics into static and motion-varying components. Next, to achieve compact yet expressive modeling, we introduce a neural contourlet representation that prunes redundant scaffolds into minimal directional bases, efficiently capturing essential geometric and motion cues. Finally, we progressively re-couple these hierarchical components to generate realistic and temporally coherent 4D LiDAR data. Extensive experiments demonstrate that our method outperforms baselines in both quality and consistency, achieving 3.3\%, 25.0\%, 17.8\% improvements in FRD, MMD, and JSD, respectively, over the strong competitors, LiDMs and RangeLDM.

Improving LLM performance on downstream tasks sometimes requires leveraging auxiliary datasets during post-training. In practice, however, developers face constraints on compute, labeling, and licensing costs that preclude using all available data, necessitating principled dataset-level selection. These constraints are increasingly shaped by dataset marketplaces, where data acquisition is governed by budgets and negotiation. We study dataset valuation as a subset selection problem during LLM post-training. Our goal is to identify and weight auxiliary datasets so as to maximize target task performance given constrained budgets. We first show that commonly used gradient alignment scores provide a reasonable yet incomplete valuation signal, as they ignore redundancy among datasets. To address this, we propose a scalable convex dataset-level valuation method based on kernel mean matching (KMM) in gradient space, which jointly accounts for alignment with the target task and redundancy across auxiliary datasets. Through extensive experiments across diverse post-training settings and tasks, we show that our approach consistently outperforms existing valuation baselines, achieving stronger performance with low computational overhead. Our results position dataset valuation as a practical decision tool for post-training data selection in market-constrained large language model settings.

We study the basic task of mean estimation in the presence of mean-shift contamination. In the mean-shift contamination model, an adversary is allowed to replace a small constant fraction of the clean samples by samples drawn from arbitrarily shifted versions of the base distribution. Prior work characterized the sample complexity of this task for the special cases of the Gaussian and Laplace distributions. Specifically, it was shown that consistent estimation is possible in these cases, a property that is provably impossible in Huber's contamination model. An open question posed in earlier work was to determine the sample complexity of mean estimation in the mean-shift contamination model for general base distributions. In this work, we study and essentially resolve this open question. Specifically, we show that, under mild spectral conditions on the characteristic function of the (potentially multivariate) base distribution, there exists a sample-efficient algorithm that estimates the target mean to any desired accuracy. We complement our upper bound with a qualitatively matching sample complexity lower bound. Our techniques make critical use of Fourier analysis, and in particular introduce the notion of a Fourier witness as an essential ingredient of our upper and lower bounds.

A central challenge in large-scale decision-making under incomplete information is estimating reliable probabilities. Recent approaches use Large Language Models (LLMs) to generate explanatory factors and coarse-grained probability estimates, which are then refined by a Naïve Bayes model over factor combinations. However, sparse factor spaces often yield ''unknown'' predictions, while expanding factors increases noise and spurious correlations, weakening conditional independence and degrading reliability. To address these limitations, we propose Anchor, an aggregated Bayesian inference framework over a hierarchical factor space. It constructs dense factor hierarchies through iterative generation and clustering, maps contexts via hierarchical retrieval and refinement, and augments Naïve Bayes with a Causal Bayesian Network to model latent factor dependencies. Experiments show that Anchor markedly reduces ''unknown'' predictions and produces more reliable probability estimates than direct LLM baselines, achieving state-of-the-art performance while significantly reducing time and token overhead.

Learning from geometrically structured data is central to applications in biology, physics, and computer vision. In many tasks, meaningful comparisons depend on how features are aligned in space. Graph Neural Networks capture local structure but are constrained by message passing. Transformers model long-range dependencies but largely ignore geometry. We introduce the Vector Bundle Attention Transformer (VBA-Transformer), a framework that redefines attention as an intrinsic geometric operator. Each token couples a base manifold coordinate with a fiber feature vector, following vector bundle theory. A principled parallel transport mechanism aligns fiber features across local coordinate systems before similarity is computed. This embeds geometry directly into the attention operator. Unlike prior methods that inject geometry as an external bias or positional encoding, VBA integrates geometry natively inside attention. On challenging single-cell RNA sequencing benchmarks, VBA achieves state-of-the-art accuracy, outperforming Transformer baselines by over 3--5\%. On spatial transcriptomics, it demonstrates superior clustering performance. On 3D point clouds, it achieves competitive accuracy, validating broad generalization across domains. Beyond empirical gains, we provide theoretical analysis of invariance and perturbation stability. We also demonstrate robust transport behavior empirically. Together, these results establish intrinsic geometric alignment as a powerful principle for scalable representation learning.

Theoretical analyses of Empirical Risk Minimization (ERM) are standardly framed within the Real-RAM model of computation. In this setting, training even simple neural networks is known to be $\exists \mathbb{R}$-complete - a complexity class believed to be harder than NP, characterizing the difficulty of solving systems of polynomial inequalities over the real numbers. However, this algebraic framework diverges from the reality of digital computation with finite-precision hardware. In this work, we analyze the theoretical complexity of ERM under a realistic bit-level model (ERM-bit), where network parameters and inputs are constrained to be rational numbers with polynomially bounded bit-lengths. Under this model, we reveal a sharp dichotomy in tractability governed by the activation function: for deep networks with any polynomial activation with rational coefficients and degree at least $2$, deciding ERM-bit is #P-hard, determining the sign of a single partial derivative is unlikely to be in BPP, and deciding a specific bit in the gradient is #P-hard. In contrast, for piecewise-linear activations such as ReLU, precision requirements remain manageable: ERM-bit is in NP, indeed NP-complete, and standard backpropagation runs in polynomial time, showing that finite-precision constraints are not merely implementation details but fundamental determinants of learnability.

Sign-based and LMO-inspired optimizers have recently attracted substantial attention in deep learning due to their strong performance and low memory footprint. However, their fixed-magnitude updates can hurt terminal convergence: they decouple update mechanisms from gradient magnitudes and fail to account for parameter heterogeneity, often leading to oscillation rather than convergence. We propose SoftSignum, a smooth relaxation of sign-based optimization that replaces the hard sign map with a temperature-controlled soft-sign transformation, enabling a parameter-wise transition from sign-like updates to magnitude-sensitive SGD-like steps. We complement it with an adaptive quantile-based temperature schedule and extend the same principle to matrix-valued optimizers, obtaining SoftMuon. We also develop a generalized geometry-relaxation framework based on strongly convex regularizers and Fenchel conjugates, proving convergence in stochastic non-convex setting. Experiments on diverse deep learning tasks, including LLM pretraining, show that SoftSignum and SoftMuon consistently improve over their hard sign-based counterparts and standard AdamW.

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this work, we propose novel non-asymptotic probabilistic uniform error bounds for kernel-based regression. Compared to related bounds in the literature that are restricted to (conditionally) independent sub-Gaussian noise, our bounds allow to consider a broad class of non-Gaussian distributions, such as sub-Gaussian, bounded, sub-exponential, and variance/moment-bounded noise. Moreover, our results apply to correlated and uncorrelated noise. We compare our proposed error bounds with existing results in terms of the induced uncertainty region and their performance in safe control, demonstrating the tightness of the proposed bounds.

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to propose draft tokens that are subsequently verified by a larger target model. However, the performance of standard SD is often limited by the strictly sequential execution of these drafting and verification stages. To address this, this paper proposes MineDraft, a batch parallel speculative decoding (PSD) framework designed to effectively hide drafting latency by overlapping it with verification. Our theoretical analysis shows that PSD is substantially more efficient than standard SD. MineDraft realizes the PSD through a novel batch-parallel design that maintains two batches of requests, overlapping drafting for one batch with verification for the other. Our experimental results show significant improvements of MineDraft in both throughput (up to 75%) and end-to-end latency (up to 39%) over standard SD. Furthermore, we have implemented MineDraft as a plugin for vLLM, demonstrating its practicality for production-ready inference systems. The code is publicly available in the [MineDraft GitHub repository](https://github.com/electron-shaders/MineDraft).

Offline reinforcement learning (RL) can fail spectacularly when bootstrapped temporal-difference (TD) updates amplify their own errors, driving the critic toward extreme and unusable Q-values. A key counterintuitive insight of this work is that collapse is not only a property of the backup rule or network architecture: the optimizer alone can directly trigger or suppress instability. From a control-theoretic viewpoint, we model offline TD learning as a feedback system and analyze Adam-based critic updates. This yields a necessary and sufficient condition for stability: training is stable if and only if the spectral radius of the update dynamics is strictly below one. Further analysis reveals that standard Adam updates can inadvertently distort the parameter geometry, necessitating explicit orthogonality constraints to prevent TD error amplification. To this end, we propose AdamO, an Adam-based optimizer with a decoupled orthogonality correction regulated by a strict task-alignment budget. We prove that this design theoretically guarantees worst-case task safety and preserves Adam’s continuous-time dissipative dynamics. Empirically, AdamO is plug-and-play across diverse offline RL baselines, improving stability and returns across a broad suite of benchmarks.

We present a regression-adjustment framework designed for the estimation of longitudinal treatment effects in randomized experiments under static regimes. While regression-adjustment methods are useful for variance reduction in randomized experiments by using pre-treatment covariates, they usually focus only on average effects, from which we cannot obtain valuable insights into when the effects appear and how long they continue. To address this issue, we consider intermediate outcomes and evolving post-treatment covariates over time, and we represent such dynamic trajectories using transition kernels. Furthermore, we establish the asymptotic normality and the semiparametric efficiency bound for our estimator, enabling more powerful statistical inference. Simulation studies and empirical analysis using A/B test data from a streaming platform in Japan show the practical advantages of our method.

High-quality data is a cornerstone of large language model (LLM) pretraining, yet its growth has not kept pace with the needs of frontier models. In this paper, we introduce RePro, a novel web recycling method that trains a relatively small LM with reinforcement learning to generate effective and faithful rephrasings of pretraining data. Specifically, we design one *quality* reward and three *faithfulness* rewards, optimizing the LM rephraser to convert organic data into high-quality rephrasings while maintaining its core semantics and structure. In our experiment, we train a rephraser as small as 1B parameters to recycle 72B tokens sampled from DCLM-RefinedWeb. Pretraining results on 400M, 1.4B, and 2.8B models demonstrate that RePro delivers 3.7\%-14.5\% relative accuracy gains over organic-only baseline on 22 downstream tasks, doubling the performance gains achieved by the state-of-the-art web recycling method that prompts a 70B rephraser. Experiments with different amounts of recycled data highlight that RePro improves organic data efficiency by 2-3$\times$. Individual and distributional analyses validate that RePro preserves more critical information and faithfully reflects the characteristics of organic data compared to prompting-based methods. Together, these results show that RePro provides an efficient and controllable path to effectively recycle organic data for pretraining. Our code is available at https://github.com/cxcscmu/RePro.

We study the sparse spiked Wigner model, where the goal is to recover an $s$-sparse unit vector $\boldsymbol{u} \in \mathbb{R}^d$ from a noisy observation $\boldsymbol{Y} = \beta \boldsymbol{u} \boldsymbol{u}^\top + \boldsymbol{W}$. While the information-theoretic threshold is $\beta = \widetilde{\Omega}(\sqrt{s})$, existing polynomial-time algorithms require $\beta = \widetilde{\Omega}(s)$, yielding a substantial computational-statistical gap. We propose a column thresholding method that attains the $\widetilde{\Omega}(\sqrt{s})$ scaling for both estimation and support recovery under the non-uniformity condition $|| \boldsymbol{u} ||_\infty = \Omega(1)$. This condition is not merely technical: it explicitly rules out uniform spikes, for which planted-clique-based hardness results apply, and identifies a concrete class of non-uniform spikes where the required signal strength can be reduced. Building on this initializer, we further develop a truncated power method that iteratively refines the estimate with provable linear convergence.