ICML 2026 论文列表

Automating formal proofs of combinatorial identities is challenging for LLM-based provers, as long-horizon proof planning is required and unconstrained search quickly explodes. Symbolic methods such as the Wilf--Zeilberger (WZ) method can achieve a mechanized proof of combinatorial identities by constructing special auxiliary functions and demonstrating that they satisfy specific recurrence relations. We propose WZ-LLM, a neuro-symbolic framework that turns WZ proof plans into executable proof sketches in Lean~4 and uses an LLM-based prover to discharge the resulting machine-checkable subgoals. We also train a dedicated WZ-Prover via a Lean-kernel-verified bootstrapping loop with expert-verified iteration, followed by DAPO-based refinement. Experiments show that WZ-LLM achieves a 34\% proof success rate on LCI-Test (100 classical combinatorial identities), outperforming strong baselines such as DeepSeek-V3 and Goedel-Prover-V2; moreover, on LCI-Test it proves 5 identities on which the symbolic-only baseline fails. WZ-LLM also improves performance on CombiBench and PutnamBench-Comb, suggesting the effectiveness of coupling symbolic proof sketches with learned formal reasoning. Experiments show that WZ-LLM achieves a 34\% proof success rate on LCI-Test (100 classic combinatorial identities), outperforming strong baselines such as DeepSeek-V3 and Goedel-Prover-V2, and delivering consistent gains on CombiBench and PutnamBench-Comb. These results indicate that our framework provides two complementary strengths: improved direct proving for identities beyond the scope of WZ, and substantially higher end-to-end success when WZ sketches guide a specialized prover.

Conditional diffusion models appear capable of compositional generalization, i.e., generating convincing samples for out-of-distribution combinations of conditioners, but the mechanisms underlying this ability remain unclear. To make this concrete, we study length generalization, the ability to generate images with more objects than seen during training. In a controlled CLEVR setting (Johnson et al., 2017), we find that length generalization is achievable in some cases but not others, suggesting that models only sometimes learn the underlying compositional structure. We then investigate locality as a structural mechanism for compositional generalization. Prior works proposed score locality as a mechanism for creativity in unconditional diffusion models (Kamb & Ganguli, 2024; Niedoba et al., 2024), but did not address flexible conditioning or compositional generalization. In this paper, we prove an exact equivalence between a specific compositional structure (*conditional projective composition*) (Bradley et al., 2025) and scores with sparse dependencies on both pixels and conditioners (*local conditional scores*). This theory also extends to compositions of concepts (such as style+content) in feature-space. We validate our theory empirically: CLEVR models that succeed at length generalization exhibit local conditional scores, while those that fail do not. Furthermore, we show that a causal intervention explicitly enforcing local conditional scores enables length generalization in a previously failing model. Finally, we investigate feature-space compositionality in color-conditioned CLEVR, and find preliminary evidence of compositional structure and corresponding local mechanisms in SDXL.

We initiate the study of *structured Stackelberg games*, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. We find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that *tightly* characterizes the leader's instance-optimal regret. We term this the *Stackelberg-Littlestone dimension*, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

Although learned representations underlie neural networks' success, their fundamental properties remain poorly understood. A striking example is the emergence of simple geometric structures in LLM representations: for example, calendar months organize into a circle, years form a one-dimensional manifold, and the latitude and longitude of cities can be decoded by low-dimensional linear probes. We show that the statistics of language exhibit a translation symmetry---e.g,. the co-occurrence probability of two months depends only on the time interval between them---and we prove that the latter governs the aforementioned geometric structures in high-dimensional word embedding models. Moreover, we find that these structures persist even when the co-occurrence statistics are strongly perturbed (for example, by removing all sentences in which two months appear together) and at moderate embedding dimension. We show that this robustness naturally emerges if the co-occurrence statistics are collectively controlled by an underlying continuous latent variable. We empirically validate this theoretical framework in word embedding models, text embedding models, and large language models.

Pretraining language models directly on web-scale corpora is the de facto paradigm. We study an alternative where the model is initially exposed to *abstract structured data* to ease the subsequent acquisition of rich semantic knowledge, much like humans learning simple logic and mathematics before higher reasoning. We focus on *procedural data*, generated by formal languages and other simple algorithms, as such abstract data. We first diagnose the algorithmic skills that different forms of procedural data can improve, often significantly. For example, the accuracy of context recall (Needle-in-a-haystack) jumps from 10 to 98% when a model is pretrained on Dyck sequences (balanced brackets). Second, we study how these gains are reflected in pretraining larger models (up to 1.3B). We find that front-loading as little as 0.1–0.3% procedural data significantly outperforms standard pretraining on natural language, code, and informal mathematics (C4, CodeParrot, and DeepMind-Math datasets). Notably, this also enables the models to reach the same loss value with only 55/67/86% of the original data and thus a comparable reduction in FLOPs. Third, we explore the mechanisms behind the benefits and find that procedural pretraining instills non-trivial structure in both attention and MLP layers. The former is particularly important for structured domains (e.g. code), and the latter for language. Finally, we lay a path for combining multiple forms of procedural data. Our results show that procedural pretraining is a simple, lightweight means of improving performance and accelerating language model pretraining, ultimately suggesting the promise of disentangling knowledge acquisition from reasoning in LLMs.

We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text. Using singular value decomposition of weight matrices, we find that CPT leaves singular value spectra largely invariant, with adaptation driven mainly by changes in singular vectors. An analysis of attention-head projection matrices reveals strong, domain-dependent **head heterogeneity**, which we exploit to define a head importance criterion: up to **60%** of head updates can be removed without measurable quality loss. Selectively rewinding low-importance heads to their pre-trained state improves benchmark accuracy by up to **4%** versus the fully trained baseline. Finally, we identify **domain connectivity**—linear interpolation between CPT checkpoints yields smooth domain-quality interpolation without notable degradation on either domain—and release Diffract, an open-source toolkit for scalable spectral analysis of billion-parameter models.

Gradient-variation online learning has drawn increasing attention due to its deep connections to game theory and optimization. It has been studied extensively in the full-information setting, but is underexplored with bandit feedback. In this work, we focus on gradient variation in Bandit Convex Optimization (BCO) with two-point feedback. By proposing a refined analysis of the *non-consecutive* gradient variation, a fundamental quantity in gradient variation with bandit feedback, we improve the dimension dependence for both convex and strongly convex functions compared with the best known results (Chiang et al., 2013). Our improved analysis of the non-consecutive gradient variation also implies other favorable problem-dependent guarantees, such as gradient-variance and small-loss regret bounds. Beyond the two-point setup, we demonstrate the versatility of our technique by achieving the *first* gradient-variation bound for one-point bandit linear optimization over hyper-rectangular domains. Finally, we validate the effectiveness of our results in more challenging tasks such as dynamic and universal regret minimization, establishing the *first* gradient-variation dynamic and universal regret bounds for two-point BCO.

Simulation has become a key tool for training and evaluating home robots at scale, yet existing environments fail to capture the diversity and physical complexity of real indoor spaces. Current scene synthesis methods produce sparsely furnished rooms that lack the dense clutter, articulated furniture, and physical properties essential for robotic manipulation. We introduce SceneSmith, a hierarchical agentic framework that generates simulation-ready indoor environments from natural language prompts. SceneSmith constructs scenes through successive stages—from architectural layout to furniture placement to small object population—each implemented as an interaction among VLM agents: designer, critic, and orchestrator. The framework tightly integrates asset generation through text-to-3D synthesis for static objects, dataset retrieval for articulated objects, and physical property estimation. SceneSmith generates 3-6x more objects than prior methods, with $<$2\% inter-object collisions and 96\% of objects remaining stable under physics simulation. In a user study with 205 participants, it achieves 92\% average realism and 91\% average prompt faithfulness win rates against baselines. We further demonstrate that these environments can be used in an end-to-end pipeline for automatic robot policy evaluation.

With the recent fast development of generative models, instruction-based image editing has shown great potential in generating high-quality images. However, the quality of editing highly depends on carefully designed instructions, placing the burden of task decomposition and sequencing entirely on the user. To achieve autonomous image editing, we present PhotoAgent, a system that advances image editing through explicit aesthetic planning. Specifically, PhotoAgent formulates autonomous image editing as a long-horizon decision-making problem. It reasons over user aesthetic intent, plans multi-step editing actions via tree search, and iteratively refines results through closed-loop execution with memory and visual feedback, without requiring step-by-step user prompts. To support reliable evaluation in real-world scenarios, we introduce UGC-Edit, an aesthetic evaluation benchmark consisting of 7,000 photos and a learned aesthetic reward model. We also construct a test set containing 1,017 photos to systematically assess autonomous photo editing performance. Extensive experiments demonstrate that PhotoAgent significantly outperforms existing methods in both instruction faithfulness and visual quality across a diverse range of editing scenarios.

Incomplete multi-view clustering is challenging due to view missingness and the entanglement of shared semantics with view-specific factors in latent representations. Existing methods often rely on heuristic fusion or direct completion strategies, which suffer from error propagation and unreliable generation under missing views. In this paper, we propose an **I**nformation-guided **D**isentangled latent modeling framework with **C**onditional **D**iffusion for incomplete multi-view clustering (IDCD). Specifically, we first encode each view into a latent representation that is variationally decomposed into a view-wise semantic latent and a view-specific factor. Information-theoretic objectives are introduced to guide the disentanglement of view-wise latents, preserving essential multi-view information while reducing the dependency between semantic and view-specific factors and encouraging cross-view semantic consistency. Besides, we aggregate the semantic latents via a mixture of Wasserstein distributions to obtain a unified global representation, where we impose a Gaussian mixture prior to explicitly couple representation learning with clustering. Based on the learned disentangled latent space, a conditional diffusion model guided by both the global semantic latent and view-specific factors is employed to generate missing views in a consistent manner. Extensive experiments on benchmark datasets demonstrate superior clustering performance and robust missing-view generation compared to state-of-the-art methods.

Standard mixed-precision training of neural networks requires many bytes of accelerator memory for each model parameter. These bytes reflect not just the parameter itself, but also its gradient and one or more optimizer state variables. With each of these values typically requiring 4 bytes, training even a 7 billion parameter model can be impractical for researchers with less than 100\,GiB of accelerator memory. We introduce FlashOptim, a suite of optimizations that reduces per-parameter memory by over 50% while preserving model quality and API compatibility. Our approach introduces two key techniques. First, we improve master weight splitting by finding and exploiting a tight bound on its quantization error. Second, we design companding functions that greatly reduce the error in 8-bit optimizer state quantization. Together with 16-bit gradients, these techniques reduce AdamW memory from 16 bytes to 7 bytes per parameter, or 5 bytes with gradient release. They also cut model checkpoint sizes by more than half. Experiments with FlashOptim applied to SGD, AdamW, and Lion show no measurable quality degradation across a collection of standard vision and language benchmarks, including Llama-3.1-8B finetuning.

Recently, it has received growing attention in building AI Scientist agents with Large Language Models (LLMs). Since scientific discovery fundamentally relies on uncovering causal relationships from observations, the capability of causal thinking that distinguish causation from correlation and hidden biases, is essential to LLM agents. Despite a number of existing benchmarks for AI scientists, they do not explicitly incorporate challenges from hidden confounders, selection bias, and noisy measurements that widely exist in real-world scientific discovery. To this end, we present CausalGame, a benchmark that evaluates the causal thinking capabilities of LLM agents through interactive games. More specifically, we ask LLM agents to actively design experimental protocols, collect observation data and derive a final solution with an explanation report. To emulate realistic scientific discovery challenges, we design 14 game settings with the incorporation of selection bias, noisy measurements, and hidden confounders. The results with 29 frontier LLM agents show that they consistently fail to reason about and recover the underlying causal relationships required to solve the games. CausalGame provides a controlled testbed for evaluating causal thinking of AI Scientist agents. The project is available at causalgame.github.io .

Recent work has shown that scaling large language models (LLMs) improves their alignment with human brain activity, yet it remains unclear what drives these gains or which representational properties are responsible. Although larger models often yield better task performance and brain alignment, they are increasingly difficult to analyze mechanistically. This raises a fundamental question: \emph{what is the minimal model capacity required to capture brain-relevant representations?} To address this question, we systematically investigate how constraining model scale and numerical precision affects brain alignment. We compare full-precision LLMs, small language models (SLMs), and compressed variants (quantized and pruned) by predicting fMRI responses during naturalistic language comprehension. Across model families up to 14B parameters, we find that 3B SLMs achieve brain predictivity indistinguishable from larger LLMs, whereas 1B models degrade substantially, particularly in semantic language regions. Brain alignment is remarkably robust to compression: most quantization and pruning methods preserve neural predictivity, with GPTQ as a consistent exception. Linguistic probing reveals a dissociation between task performance and brain predictivity: compression degrades discourse, syntax, and morphology, yet brain predictivity remains largely unchanged. Overall, brain alignment saturates at modest model scales and is resilient to compression, challenging common assumptions about neural scaling and motivating compact models for brain-aligned language modeling.

Uniform Discrete Diffusion Model (UDM) has recently emerged as a promising paradigm for discrete generative modeling; however, its integration with reinforcement learning remains largely unexplored. We observe that naively applying GRPO to UDM leads to training instability and marginal performance gains. To address this, we propose **UDM-GRPO**, the first framework to integrate UDM with RL. Our method is guided by two key insights: (i) treating the final clean sample as the action provides more accurate and stable optimization signals; and (ii) reconstructing trajectories via the diffusion forward process better aligns probability paths with the pretraining distribution. Additionally, we introduce two strategies, Reduced-Step and CFG-Free, to further improve training efficiency. **UDM-GRPO** significantly improves base model performance across multiple T2I tasks. Notably, GenEval accuracy improves from $69\\%$ to $96\\%$ and PickScore increases from $20.46$ to $23.81$, achieving state-of-the-art performance in both continuous and discrete settings. On the OCR benchmark, accuracy rises from $8\\%$ to $57\\%$, further validating the generalization ability of our method. Code is available at https://github.com/Yovecent/UDM-GRPO.

Treatment responder classification seeks to learn a rule to classify individuals who will benefit from the treatment. This paper studies a new scenario in treatment responder classification when abstention is allowed, i.e., practitioners can opt out of making uncertain classification on some individuals for further investigation. By revealing the implicit relation between causal misclassification risk with abstention and Conditional Value at Risk (CVaR), we develop a doubly robust method named TRECA to learn the classification rule under loose convergence conditions on nuisance parameters, and further extend it to deal with possible violation on key assumptions such as monotonicity and unconfoundedness. Rigorous theories and extensive experiments on two real-world datasets demonstrate the theoretical and experimental guarantee on our methods in learning treatment responders classification rules with low regret at the cost of limited abstention.

Enhancing Large Reasoning Models (LRMs) for specialized domains remains a critical challenge. While recent industrial frameworks attempt to encapsulate Standard Operating Procedures into modular "skills" for dynamic retrieval, utilizing them via context engineering often proves insufficient for complex workflows, leading to "Cognitive Drift." To mitigate this, we propose $\textbf{Thought Guidance-Retrieval Augmented Generation (TG-RAG)}$, a Retrieval-Augmented framework that effectively steers the generation process without relying solely on the model's self-correction. Built upon an Expert Procedure Graph (EPG) that formalizes unstructured SOPs, the framework uniquely employs a dynamic $\textbf{``Interrupt-Retrieve-Generate" (IRG)}$ mechanism to actively inject step-specific directives into the model's reasoning process. Extensive evaluations show that TG-RAG achieves competitive performance, demonstrating advantages in specialized domains by ensuring faithful adherence to domain SOPs. Code is available at https://github.com/V1ncent-S/Thought-Guidance.

Continual learning is a long-standing challenge in robot policy learning, where a policy must acquire new skills over time without catastrophically forgetting previously learned ones. While prior work has extensively studied continual learning in relatively small behavior cloning (BC) policy models trained from scratch, its behavior in modern large-scale pretrained Vision-Language-Action (VLA) models remains underexplored. In this work, we find that pretrained VLAs are remarkably resistant to forgetting compared with smaller policy models trained from scratch. Simple Experience Replay (ER) works surprisingly well on VLAs, sometimes achieving zero forgetting even with a small replay data size. Our analysis reveals that pretraining plays a critical role in downstream continual learning performance: large pretrained models mitigate forgetting with a small replay buffer size while maintaining strong forward learning capabilities. Furthermore, we find that VLAs can retain relevant knowledge from prior tasks despite performance degradation during learning new tasks. This knowledge retention enables rapid recovery of seemingly forgotten skills through finetuning. Together, these insights imply that large-scale pretraining fundamentally changes the dynamics of continual learning, enabling models to continually acquire new skills over time with simple replay.

Entropic optimal transport (EOT) via Sinkhorn iterations is widely used in modern machine learning, yet GPU solvers remain inefficient at scale. Tensorized implementations suffer quadratic HBM traffic from dense $n\times m$ interactions, while existing online backends avoid storing dense matrices but still rely on generic tiled map-reduce reduction kernels with limited fusion. We present **FlashSinkhorn**, an IO-aware EOT solver for squared Euclidean cost that rewrites stabilized log-domain Sinkhorn updates as row-wise LogSumExp reductions of biased dot-product scores, the same normalization as transformer attention. This enables FlashAttention-style fusion and tiling: fused Triton kernels stream tiles through on-chip SRAM and update dual potentials in a single pass, substantially reducing HBM IO per iteration while retaining linear-memory operations. We further provide streaming kernels for transport application, enabling scalable first- and second-order optimization. On A100 GPUs, FlashSinkhorn achieves up to $32\times$ forward-pass and $161\times$ end-to-end speedups over state-of-the-art online baselines on point-cloud OT, improves scalability on OT-based downstream tasks. For reproducibility, we release an open-source implementation at https://github.com/ot-triton-lab/flash-sinkhorn.

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) reduce variance while maintaining tractability by leveraging low-dimensional individual state and action spaces and known transition dynamics to compute the exact expected return conditioned on Monte Carlo rollouts of common noise. However, HSMs have not been extended to partially observable settings. We propose *Recurrent Structural Policy Gradient* (RSPG), the first history-aware HSM for MFGs with public partial information. RSPG achieves an order-of-magnitude faster convergence than model-free RL methods while learning history-aware behaviour, unlike current HSMs. To facilitate research into MFGs, we also introduce MFAX, our JAX-based framework for MFGs that supports both analytic and sample-based mean-field updates.