ICML 2026 Papers

Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models. By explicitly minimizing the sharpness of the loss landscape, SAM often improves generalization while delivering strong empirical performance. However, SAM and its variants, like most training algorithms, are sensitive to the choice of learning rate, which is typically selected through extensive hyperparameter tuning or predefined schedulers. In this work, motivated by recent advances on the effectiveness of stochastic Polyak step sizes for Stochastic Gradient Descent (SGD), we derive Polyak schedulers tailored to SAM-style updates, yielding novel adaptive algorithms in both deterministic and stochastic settings. In the smooth setting, we prove linear convergence for strongly convex objectives and an $\mathcal{O}(1/T)$ convergence rate for convex objectives in the deterministic case. In the stochastic setting, we establish analogous convergence guarantees up to a neighborhood of the optimum. Numerical experiments demonstrate that the proposed Polyak schedulers achieve performance comparable to or better than carefully tuned SAM baselines, while substantially reducing the need for learning-rate tuning.

While benchmarks measure the accuracy of LLM-powered agents, they mostly assume full automation, failing to represent the collaborative nature of real-world use cases. In this paper, we make two major steps towards the rigorous assessment of human-agent interactions. First, we propose PULSE, a framework for more efficient human-centric evaluation of agent designs, which comprises collecting user feedback, training an ML model to predict user satisfaction, and computing results by combining human satisfaction ratings with model-generated pseudo-labels. Second, we deploy PULSE n software engineering---one of the highest-impact, real-world domains for LLM agents---via a large-scale web platform built around the open-source agent OpenHands. Across 15k users, we evaluate how three agent design decisions impact developer satisfaction rates. We also show how PULSE can lead to more robust conclusions about agent design, reducing confidence intervals by 40% compared to a standard A/B test. Finally, we find substantial discrepancies between in-the-wild results with benchmark performance (e.g., the anti-correlation between claude-sonnet-4 and gpt-5, underscoring the limitations of benchmark-driven evaluation. Our framework PULSE provides guidance for future evaluations, and our findings identify opportunities for better software agent designs.

Motivated by recent work on benign overfitting in overparameterized machine learning, we study the generalization behavior of functions in Sobolev spaces $W^{k, p}(\mathbb{R}^d)$ that perfectly fit a noisy training data set. Under assumptions of label noise and sufficient regularity in the data distribution, we show that approximately norm-minimizing interpolators, which are canonical solutions selected by smoothness bias, exhibit harmful overfitting: even as the training sample size $n \to \infty$, the generalization error remains bounded below by a positive constant with high probability. Our results hold for arbitrary values of $p \in [1, \infty)$, in contrast to prior results studying the Hilbert space case ($p = 2$) using kernel methods. Our proof uses a geometric argument which identifies harmful neighborhoods of the training data using Sobolev inequalities.

Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the **noise-to-signal ratio** (NSR) of a policy-gradient estimator, defined as the estimator variance (noise) normalized by the squared norm of the true gradient (signal). Our main result is that, for (i) finite-horizon linear systems with Gaussian policies and linear state-feedback, and (ii) finite-horizon polynomial systems with Gaussian policies and polynomial feedback, the NSR of the REINFORCE estimator can be characterized exactly—either in closed form or via numerical moment-evaluation algorithms—without approximation. For general nonlinear dynamics and expressive policies (including neural policies), we further derive a general upper bound on the variance. These characterizations enable a direct examination of how NSR varies across policy parameters and how it evolves along optimization trajectories (e.g. SGD and Adam). Across a range of examples, we find that the NSR landscape is highly non-uniform and typically increases as the policy approaches an optimum; in some regimes it blows up, which can trigger training instability and policy collapse.

While frontier formal mathematics systems now routinely develop repository-scale proof engineering artifacts requiring multi-file coordination and semantic correctness beyond compilation, existing evaluation benchmarks remain focused on isolated theorem proving. We introduce Automated Proof Engineering (APE), the first systematic framework for evaluating repository-scale proof engineering through dual verification that validates both syntactic compilation and semantic requirement satisfaction in pinned library environments. We present a complete infrastructure comprising APE-Bench, which automatically extracts proof engineering tasks from real library commit histories, and APE-Harness, a unified execution framework based on task contract abstraction. This contract-based design enables standardized evaluation across diverse formal mathematics tasks and fair systematic comparison of different agent implementations (including our APE-Agent reference scaffold alongside Claude Code and Codex CLI) on identical task specifications. We demonstrate the framework's effectiveness through comprehensive evaluation. All code, benchmarks, and infrastructure will be open-sourced.

Compositional generalization is essential for reaching unseen goals under novel contextual variations in offline goal-conditioned reinforcement learning (GCRL), where a generalist goal-reaching agent must be learned from limited data. Most prior approaches pursue this via trajectory stitching over temporally contiguous segments, which limits composing behaviors across varying contexts. To overcome this limitation, we formalize *analogy transduction* as synthesizing new plans by composing task-endogenous analogies with given contexts and propose a novel analogy representation tailored for it. Grounded in our theory, this analogy representation captures what changes under optimal task execution, remains invariant to contextual variations, and is sufficient for optimal goal reaching. We further contend that generalization to unseen analogy-context pairs is a practical obstacle in analogy transduction, and introduce a new approach for offline GCRL that enables analogy transduction beyond seen pairs to unseen combinations. We empirically demonstrate the effectiveness of our approach on OGBench manipulation environments, substantially outperforming prior methods that do not perform analogy transduction.

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of standard functions, a process that requires expert knowledge, results in limited adaptivity to data, and imposes strong assumptions on the hypothesis space. Re-evaluating this challenge from a hierarchical Bayesian and function-space view, we study Empirical GPs, a principled framework for constructing flexible, data-driven GP priors that overcome these limitations. Rather than relying on standard parametric kernels, we estimate the mean and covariance functions empirically from a corpus of historical observations, enabling the prior to reflect rich, non-trivial covariance structures present in the data. Theoretically, we show that the resulting model converges to the GP that is closest (in KL-divergence sense) to the real data-generating process. We formulate the problem of learning the GP prior from independent datasets as maximum likelihood estimation and derive an Expectation-Maximization algorithm with closed-form updates, allowing the model handle heterogeneous observation locations across datasets. We demonstrate that Empirical GPs achieve competitive performance on learning curve extrapolation and time series forecasting benchmarks.

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.

Parameter sharing is a widely used technique in Multi-Agent Reinforcement Learning (MARL) that enhances sample efficiency by equipping agents with a unified policy. While effective in homogeneous settings, it often struggles in heterogeneous environments where agents possess diverse capabilities. Conversely, learning customized policies for agents can resolve knowledge conflicts but significantly hinders knowledge transfer, thereby reducing learning efficiency. Existing approaches attempt to balance this trade-off using clustering or agent-specific masks, but they typically rely on strong environment-specific priors and struggle in settings where the team exhibits multi-modal policies. To address these limitations, we propose Dspic, an efficient shared-policy algorithm grounded in the maximum entropy framework. Specifically, Dspic employs self-supervised learning to extract discriminative role embeddings for each agent. These embeddings guide a complete division of the observation space, providing a theoretical guarantee for the optimality of parameter sharing. Furthermore, to handle the increased observation complexity and diversity resulting from this division, Dspic incorporates a diffusion policy, enhancing the capacity to model complex action distributions while enabling efficient learning. Extensive experiments on MaMuJoCo, SMAC, SMACv2, and LBF demonstrate that Dspic achieves superior sample efficiency while maintaining asymptotic optimality.

Watermarking methods embed imperceptible and verifiable signals into text generated by large language models (LLMs). Existing approaches include zero-bit schemes for distinguishing synthetic text from human writing and multi-bit schemes for embedding metadata. However, current multi-bit watermarking methods do not allow selective disclosure: verifying any part of the watermark requires revealing the entire embedded message. This lack of control leads to unnecessary information exposure and raises privacy concerns. We propose Hierarchical Vocabulary Routing (HeRo), a watermarking framework that enables selective disclosure of embedded metadata. The method recursively partitions the vocabulary and distributes watermark information across hierarchical layers, so that different verifiers can decode only the portions of the payload corresponding to their access level. We show that the proposed scheme preserves the unbiasedness of the underlying sampling process and thus maintains text quality. Experiments demonstrate that our framework supports fine-grained access control while achieving high detection accuracy and low latency. Code is available at \url{https://github.com/xuyangc03/hero-watermark}.

Defocus deblurring in pathological microscopy remains challenging due to the spatially varying and locally discontinuous nature of optical blur induced by a position-dependent integral imaging process. Existing deep learning methods, constrained by shift-invariance assumptions and limited interpretability, are not well suited to such heterogeneous blur patterns. Neural operators provide a principled alternative by modeling defocus formation directly as an integral operator, offering a new perspective on defocus deblurring. However, most existing neural operator architectures for low-level vision rely on globally parameterized kernels that assume smoothness and stationarity, limiting their ability to model heterogeneous and locally discontinuous blur patterns. To address this limitation, we propose the Discontinuous Galerkin Neural Operator (DGNO), which parameterizes the integral kernel using a discontinuous Galerkin formulation with element-local volume operators and interface numerical fluxes. DGNO provides a principled combination of locality, heterogeneity modeling, and global coherence while preserving the underlying physics of optical image formation. Extensive experiments demonstrate that DGNO surpasses state-of-the-art methods, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance.

Recovering 3D human poses for multiple individuals from different camera views is a fundamental bottleneck for analyzing interacting behaviors. Existing self-supervised approaches leverage synthetic catalogues of 3D poses; however, this leads to poor generalization in real-world scenarios due to distribution shifts. We therefore introduce DisPOSE, a self-supervised framework that approximates the inherently discrete multi-view person-assignment problem as a generative diffusion process over the space of polystochastic tensors. By employing differentiable Sinkhorn projections during denoising, our model learns to guide solutions toward valid and feasible assignments based on 2D image priors. The complete 3D skeletons of localized individuals are then regressed using a Hypergraph-Convolutional Decoder that explicitly models relational structures and articulated joints across multiple views. The proposed approach outperforms current state-of-the-art self-supervised methods on standard datasets and demonstrates strong performance on a newly proposed benchmark featuring highly occluded scenes from surgical operating rooms. Our diffusion-based localization demonstrates high label efficiency, retaining 99\% of its performance with only 10\% of the pseudo-labels. Notably, disentangling the assignment and root regression components while maintaining differentiability makes DisPOSE nearly agnostic to different camera arrangements.

Despite the fast progress of Neural Combinatorial Optimization (NCO) on graphs, existing solvers mainly learn a narrow task (e.g., uniform TSP) at a time and hardly handle instances over diverse distributions. This paper proposes M$^2$GenCO, a **M**ulti-task learning framework that pioneers the instantiation of the **M**eta-learning mechanism with diffusion-based **Gen**erative solving for **CO** Problems (COPs) on graphs, first formulating "tasks" in meta-learning as distinct problem types instead of instances of the same problem. With a tailored lightweight graph neural network, our framework performs effective joint pre-training on a variety of problem types and efficient fine-tuning to adapt for out-of-distribution scenarios. Further, we establish a benchmark comprising 5 classic graph COPs with varying scales and multiple distributions, forming 38 distinct test datasets that facilitate standard evaluation of generalizability and adaptability for NCO solvers. Empirically, M$^2$GenCO with greedy decoder yields an overall 9.16\% performance gain with an average 95.6$\times$ acceleration for inference, and achieves concrete state-of-the-arts on all test sets with simple local searchers, maintaining superior solving time against previous neural methods. The computational resource and time consumption for training are saved by up to 82% and 91%, respectively.

Discrete diffusion models have recently emerged as a compelling alternative for language generation, enabling efficient non-autoregressive sampling while achieving strong empirical performance. A key design choice in discrete diffusion---absent in most continuous diffusion formulations---is the forward corruption kernel, with masked/absorbing corruption now dominating practice. Despite this empirical preference, there is limited statistical theory explaining when and why masking should outperform alternative kernels such as uniform replacement. In this paper, we take a step toward closing this gap from a statistical learning perspective. Our analysis establishes generalization bounds and, through an explicit comparison across different forward corruption kernels, reveals a central advantage of masking: it scales with the effective data support rather than the full ambient state space, thereby mitigating the curse of state space cardinality. We further derive structure-aware refinements that capture how concentration and sparsity in real sequential data sharpen the sample complexities. Together, these results offer a principled explanation for the empirical strength of masked diffusion and provide guidance for forward-kernel design in discrete generative modeling.

Robust conformal prediction (RCP) extends conformal prediction (CP) to noisy inputs by producing prediction sets with guaranteed coverage, ensuring that the true label is contained in the set with a user-specified probability even under worst-case perturbations. Recent works use randomized smoothing, as it provides robustness for black-box models at larger radii. Currently, there exist two setups for smoothing-based RCP: one requires extensive Monte Carlo sampling at calibration and test time but results in smaller prediction sets; the other setup produces larger prediction sets but uses a single sample at both stages. In deployment, calibration—as a one-time pre-processing step—can accommodate substantially higher computational overhead than inference. Inspired by this observation, we introduce an RCP framework that strikes a balance between the two extremes of this trade-off: we increase the sample rate at calibration time while keeping it either one or very low during test time. This calibration-time sampling opens the possibility of reducing the size of the prediction sets. In production, where the number of test predictions typically far exceeds the size of the calibration set, our Front-Loaded RCP matches the computational complexity of the state of the art while producing considerably smaller prediction sets at larger radii.

Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice. We bridge this gap by analyzing standard transformer decoders with softmax attention and rounding of activations and attention weights, while allowing depth and width to grow logarithmically with the context length. As an intermediate step, we construct hardmax transformers with ternary activations and well-separated attention scores that simulate Turing machines using Chain-of-Thought (CoT). This lets us convert the constructions to equivalent softmax transformers without the unrealistic parameter magnitudes or activation precision that prior approaches would require. Using the same technique, we analyze a recently proposed summarized CoT paradigm and show that it simulates Turing machines more efficiently, with model size scaling logarithmically in a space bound rather than a time bound. We empirically test predictions made by our results on a Sudoku reasoning task and find better alignment with learnability than for prior high-precision results. Our code is available at https://github.com/moritzbroe/transformer-expressivity.

We propose a novel framework for measuring privacy from a Bayesian game-theoretic perspective. This framework enables the creation of new, purpose-driven privacy definitions that are rigorously justified, while also allowing for the assessment of existing privacy guarantees through game theory. We show that pure and probabilistic differential privacy are special cases of our framework, and provide new interpretations of the post-processing inequality in these settings. Further, we demonstrate that privacy guarantees can be established for deterministic algorithms, which are overlooked by current privacy standards.

Accurate climate forecasting provides critical support for decision-making in agriculture, energy, and disaster preparedness. Current deterministic models often fail to capture climate uncertainty, while existing generative approaches oversimplify the system by neglecting key spatiotemporal dependencies and cross-scale interactions. To address these limitations, we introduce ClimateAR, an AutoRegressive generative model for probabilistic seasonal-to-interannual Climate forecasting. The framework incorporates two novel components: (1) an aligned tokenizer that bridges and aligns heterogeneous simulation and real-world data to improve transferability across domains, and (2) a mixed-scale conditioning mechanism that captures multi-scale climate interactions for robust probabilistic forecasting. Extensive evaluations on the ERA5 reanalysis dataset show that ClimateAR achieves state-of-the-art performance, improving anomaly correlation skill by 37.56\% on average compared to leading baselines.

Masked Diffusion Models (MDMs) as language models generate by iteratively unmasking tokens, yet their performance crucially depends on the inference-time order of unmasking. Conventional methods such as confidence-based sampling are short-sighted, focusing on local optimization which neglects test-time computation and allows early decoding errors to cascade. We propose Lookahead Unmasking (LookUM), which addresses these concerns by guiding sampling path with a verifier over alternative unmasking orders, without requiring an external reward model. Our framework couples (i) a path generator that proposes paths by sampling from pools of unmasking sets with (ii) a verifier that computes the uncertainty of the proposed paths and performs importance sampling to subsequently select the final paths. Erroneous unmasking inflates sequence-level uncertainty, and our method exploits this to avoid error-prone trajectories. We validate our framework across six benchmarks, such as mathematics, planning, and coding, and demonstrate consistent performance improvements. LookUM requires only two to three paths to achieve peak performance. LLaDA with LookUM matches the performance of RL-tuned LLaDA 1.5 and yields additional gains when applied to LLaDA 1.5, suggesting complementarity with reinforcement learning.