ICML 2026 Papers

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Competitive programming problems are increasingly used to evaluate the coding capabilities of large language models (LLMs) due to their complexity and ease of verification. Yet, current coding benchmarks face limitations such as a lack of exceptionally challenging problems, insufficient test case coverage, and reliance on online platform APIs that limit accessibility. To address these issues, we introduce LiveOIBench, a large-scale competitive programming benchmark featuring $403$ expert-curated problems, averaging $60$ official test cases each, drawn from 72 contests across 14 Informatics Olympiads held between 2023 and 2025. LiveOIBench has four key features: (1) expert-designed tasks with detailed subtask rubrics and extensive test cases; (2) direct comparison to elite human contestants; (3) continuous updates to reduce contamination risk; and (4) a fully offline, reproducible evaluation system. Benchmarking $34$ popular general-purpose and reasoning LLMs, we find that GPT-5 achieves an 81.76th percentile, still falling short of top human contestants, while among the open-weight models, GPT-OSS-120B reaches only the 60th percentile. Reasoning-trace analyses indicate that robust reasoning models prioritize precise problem analysis over excessive exploration. Finally, analyses across release dates, task familiarity, and code similarity find minimal evidence of data contamination in our benchmark. Our leaderboard, code, and data are available at: https://liveoibench.github.io/.

Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative example, we consider Kalai's algebraic Hirsch conjecture and recast the construction of its counterexamples as a sparse-reward reinforcement learning problem on graphs. We propose a constrained options-based HRL framework with an equivariant graph neural network policy, which allows us to learn useful temporal abstractions for this task. We evaluate our approach over a wide range of degrees and demonstrate that it consistently outperforms classical RL algorithms as well as greedy search. By exploiting the hierarchical structure of the problem, we effectively provide a first-of-its-kind application of HRL to a problem in commutative algebra.

Despite the rapid development of AI reviewers, evaluating such systems remains challenging: metrics favor overlap with human reviews over correctness. However, since human reviews often cover only a subset of salient issues and sometimes contain mistakes, they are unreliable as gold references. To address this, we build category-specific benchmark subsets and skip evaluation when the corresponding human reviews are missing to strengthen ***Co***mpleteness. We also leverage reviewer--author--meta-review discussions as expert annotations and filter unreliable reviews accordingly to strengthen ***Co***rrectness. Finally, we introduce `CoCoReviewBench`, which curates 3,900 papers from ICLR and NeurIPS to enable reliable and fine-grained evaluation of AI reviewers. Analysis shows that AI reviewers remain limited in correctness and are prone to hallucinations, and highlights reasoning models as more effective reviewers, motivating further directions for improving AI reviewers. Benchmarks and models are available at <https://github.com/hexuandeng/CoCoReviewBench>.

Test-time adaptation (TTA) can reduce error on new and different data by updating the model on these inputs during inference. However, these updates raise the issue of privacy w.r.t. the testing data, because the model parameters now depend on all past inputs. To control this privacy risk, we cast multiple popular TTA methods (Tent, EATA, SAR, DeYO, and COME) into differential privacy (DP) forms that apply per-sample gradient clipping and Gaussian noise for all updates. On ImageNet-C, our DP-TTA methods provide adequate privacy at small cost to accuracy, and in the low-privacy regime the clipping mechanism of DP can even improve the accuracy and stability of adaptation in the continual setting. These improvements to privacy and accuracy come at only modest computational overhead. These first results on private TTA raise awareness of the issue, inform the development of more private test-time updates, and identify per-sample clipping as an effective technique for improving the accuracy and stability of adaptation.

Verifying whether a language model is genuinely reasoning or pattern-matching remains an open problem: learned verifiers are expensive, and output-based heuristics are brittle. We show that valid mathematical reasoning induces a measurable, training-free spectral signature in transformer attention. By treating each attention matrix as a weighted token graph, we extract four diagnostics: Fiedler value, High-Frequency Energy Ratio (HFER), spectral entropy, and smoothness, that require no learned parameters. Experiments across seven models from four architectural families yield effect sizes up to Cohen's $d = 3.30$ ($p < 10^{-116}$), enabling $85$-$96$% single-threshold classification accuracy. Two findings sharpen the interpretation. First, \emph{Platonic validity}: the spectral signal tracks logical coherence rather than compiler acceptance, proofs rejected for timeouts or missing imports are correctly classified as valid, a distinction confirmed by a manual audit ($\kappa = 0.82$, $n = 51$). Second, \emph{architectural determinism}: Sliding Window Attention shifts the discriminative feature from HFER to smoothness ($d = 2.09$, $p < 10^{-48}$), showing that attention design governs which spectral channel encodes reasoning quality. Causal ablation confirms the signature traces induction-head circuits. The method generalises to informal chain-of-thought ($d = 0.78$, $p < 10^{-3}$), and in proof search, HFER reranking improves Best-of-16 Pass@1 by $+4.4$-$6.6$%, matching $98$% of the AUC of fully supervised probes with zero labels. Spectral graph analysis is a principled, architecture-aware primitive for reasoning verification.

Hallucinations pose a key challenge for large language models, and chain-of-thought prompting exposes intermediate reasoning but usually treats traces as linear sequences, making crossstep dependencies and unsupported intermediate claims difficult to identify. We propose a structural reasoning model to describe interactions among local reasoning steps. To detect hallucinations, we extract a directed acyclic reasoning graph over conditions and intermediate claims, verify each claim against its parent nodes, and aggregate the step signals with a simple mass-flow rule. Under a probabilistic erasure-gate abstraction, we interpret this aggregation as measuring information loss along the reasoning graph. Experiments on GSM8K, MATH, HumanEval, and HotpotQA show that the proposed method is most advantageous on longer, dependency-rich reasoning traces such as math and code generation, while remaining competitive on shorter factual QA; these results provide a structured perspective on chain-of-thought evaluation. All code and data are available at https://github.com/soncheinbok/FlowScore.

Reasoning models enhance performance by tackling problems in a step-by-step manner, decomposing them into sub-problems and exploring long chains of thought before producing an answer. However, applying extended reasoning to every step introduces substantial redundancy, as sub-problems vary widely in difficulty and complexity: a small number of pivotal steps are genuinely challenging and decisive for the final answer, while many others only involve straightforward revisions or simple computations. Therefore, a natural idea is to endow reasoning models with the ability to adaptively respond to this variation, rather than treating all steps with the same level of elaboration. To this end, we propose MixReasoning, a framework that dynamically adjusts the depth of reasoning within a single response. MixReasoning enables fine-grained mode switching by training a lightweight concise LoRA adapter and control its strength to trigger switches based on reasoning difficulty estimated from sliding-window token confidence, yielding human-like transitions between fast and slow reasoning. The resulting chain of thought then becomes a mixture of detailed reasoning on difficult steps and concise inference on simpler ones. Experiments on AIME24, MATH-500, GPQA, and GSM8K demonstrate that MixReasoning shortens reasoning length by 13\%--49\% across benchmarks of varying difficulty, delivering consistent efficiency gains while maintaining performance.

While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.

Agentic reinforcement learning has advanced large language models (LLMs) to reason through long chain-of-thought trajectories while interleaving external tool use. Existing approaches assume a fixed inventory of tools, which limits the adaptability of LLM agents to new or evolving toolsets. We present AutoTool, a training framework that equips LLM agents with dynamic tool-selection capabilities throughout their reasoning trajectories. AutoTool employs a dual-phase optimization pipeline: (i) SFT and RL-based trajectory stabilization for coherent reasoning, and (ii) KL-regularized Plackett–Luce Ranking to refine consistent multi-step tool selection. We further build a 200k dataset with explicit tool-selection rationales across 1,000+ tools and 100+ tasks spanning mathematics, science, code generation, and multimodal reasoning. Across ten diverse benchmarks, we train two base models, Qwen3-8B and Qwen2.5-VL-7B, with AutoTool. With fewer parameters, AutoTool consistently outperforms advanced LLM agents and tool-integration methods, yielding average gains of 6.4\% in math \& science reasoning, 4.5\% in search-based QA, 7.7\% in code generation, and 6.9\% in multimodal understanding. In addition, AutoTool exhibits stronger generalization by dynamically leveraging unseen tools from evolving toolsets during inference.

Multi-objective protein design is essential for meeting the complex demands of synthetic biology. To adapt to shifting multi-functional targets without the prohibitive cost of retraining, test-time scaling has emerged as a flexible, training-free alternative. However, current test-time diffusion methods face critical challenges: i) ineffective learning from interaction history leading to repetitive design errors, ii) over-reliance on successful cases as the reward signal, and iii) difficulties in balancing multi-objective functional trade-offs . To address these limitations, we propose MoMST, a framework for Multi-objective protein design via Memory-aware Self-contrastive learning with Test-time scaling in diffusion models. At test time, we develop a memory bank to extract generalizable reasoning experience from historical iterations. Building on this powerful experience learner, we derive rich residue-level relative preference signals from both successful and failed cases via self-contrastive learning for guiding protein generation. To ensure balance among competing multi-objective functions, we present an inference-time Pareto alignment strategy to resolve objective conflicts. Evaluations on both single-objective and complex multi-objective tasks demonstrate the remarkable performance of MoMST, with code available at https://github.com/MingYangi/MoMST.

New AI accelerators with novel instruction set architectures (ISAs) often require developers to manually craft low-level kernels — a time-consuming and error-prone process that does not scale across hardware targets. This delays emerging hardware platforms from reaching the market. While prior LLM-based code generation has shown promise in mature GPU ecosystems, it remains unclear whether agentic LLM systems can quickly produce valid and efficient kernels for emerging hardware with new ISAs. We present KernelCraft: the first benchmark for evaluating an LLM agent's ability to generate and optimize low-level kernels for customized accelerators through a function-calling, feedback-driven workflow. We evaluate agent performance across three emerging accelerators on more than 20 machine-learning tasks, each with five diverse task configurations. Across four leading reasoning models, the strongest agents generate functionally correct kernels for unseen ISAs within a few refinement steps, and produce optimized kernels that match or outperform compiler baselines. These results demonstrate KernelCraft's potential to accelerate the accelerator chip development cycle. KernelCraft is available at https://kernelcraft-cam.github.io/.

Large language models (LLMs) inevitably encounter distribution shifts during real-world deployment, leading to performance degradation. Although test-time learning (TTL) adapts LLMs from unlabeled test streams, applying entropy minimization to autoregressive generation faces two challenges: (i) early decoding errors can steer later tokens off track, and updating on them can push the model further off course, and (ii) updates on unreliable tokens can amplify confident error predictions and trigger model collapse. To address these challenges, we propose Future-Gain Guided Test-Time Learning (FG-TTL) for LLMs, which learns selectively from the model's own generations. Our key idea is to update only on tokens that reduce uncertainty in subsequent generation rather than tokens that are merely uncertain at the current step. Specifically, we develop a Future-Gain Guided Token Selection (FTS) strategy to decide where to learn. We introduce Future-Gain as a token-level metric for this purpose and update the model only on high-gain tokens, concentrating learning on informative positions and mitigating temporal error propagation. In addition, we design a Risk-Aware Adaptation (RAA) mechanism that controls how strongly to update by combining gain-based weighting with adaptive temperature scaling based on intrinsic uncertainty, suppressing unreliable gradients while enabling stronger learning on high-gain tokens. Experiments on six benchmarks with three LLM backbones show that FG-TTL achieves the best average performance.

While large language models (LLMs) have emerged as powerful decision-makers across a wide range of single-agent and stationary environments, fewer efforts have been devoted to settings where LLMs must engage in \emph{repeated} and \emph{strategic} interactions with unknown or dynamic opponents. In such settings, recipes built upon \emph{offline} pre-training or fine-tuning, though robust against worst-case adversaries, do not fully exploit the capability of LLMs to adapt \emph{online} based on interaction feedback. Instead, we explore the more natural perspective of \emph{scaling inference-time computation} as a mechanism for adaptation, embedding the principles of a classical game-theoretical learning dynamic, \emph{smooth Fictitious Play (sFP)}, into LLM inference: (i) for belief formation, we employ an auxiliary opponent model that in-context learns to imitate the \emph{time-averaged} behavior of the opponent; (ii) for best response, we advance best-of-$N$ (BoN) sampling by simulating against the opponent model. Empirical evaluations on two distinct forms of repeated negotiation games demonstrate that our method enables significant performance improvement over online interaction compared to various baselines, offering a scalable and principled approach to strategic decision-making without any parameter updates.

Large Vision-Language Models (LVLMs) have demonstrated remarkable capabilities in multimodal reasoning. However, prevailing reinforcement learning (RL) paradigms lack explicit counterfactual enhancement and causal learning mechanisms. This fundamental deficiency results in severe grounding failures, manifesting as a tendency to ignore visual evidence in favor of language priors or exhibiting hallucination drift during long chain-of-thought reasoning. To address this root cause, we propose CounterFactual Policy Optimization (CFPO), a novel framework that enforces causal consistency between visual perception and textual reasoning. CFPO introduces a cross-modal counterfactual enhancement mechanism, which regularizes the policy by maximizing the discrepancy between the model’s predictions and those from a counterfactual state where critical visual cues are suppressed. This approach seamlessly integrates with standard algorithms like GRPO and DAPO without requiring external reward models or additional supervision. Extensive experiments demonstrate that CFPO significantly improves reasoning fidelity, achieving consistent gains of 3.17%-6.25% over standard RL baselines and 1.32%-2.13% over the state-of-the-art perception-aware method (PAPO). Code is available at https://github.com/Raven-July/CFPO.

Test-time adaptation (TTA) adapts pretrained models to test data on-the-fly. Current TTA methods have focused on what to adapt: lightweight domain-aware components (prompts, normalization statistics) updated with consistency-aware self-supervised losses. This work investigates the more fundamental yet underexplored optimization process, providing insights and guidelines on how to appropriately update models for TTA. By analyzing the optimization error during TTA, we identify a pivotal stability-plasticity trade-off: the model should adapt to novel distributions while retaining learned knowledge, which motivates our design of a CONfidence-and-Gradient-Aware scheduler (CONGA) to constrain model learning rate (LR) within an adaptive exploration interval. For each iteration, the lower bound encourages model exploration on informative confident samples, while the upper bound prevents aggressive overfitting to noisy optimization gradients. Based on our theoretical findings, an adaptation-progress-conditioned cosine decay function decides the specific LR within the interval. As an LR scheduler, CONGA is naturally applicable on existing TTA methods as a plug-in module, introducing little computation overheads. Extensive experiments and analysis demonstrate the superiority and validness of CONGA.

Multi-agent debate (MAD) systems improve LLM reasoning through iterative deliberation, but remain vulnerable to debate collapse, a failure type where final agent decisions are compromised on erroneous reasoning. Existing methods lack principled mechanisms to detect or prevent such failures. To address this gap, we first propose a hierarchical metric that quantifies behavioral uncertainty at three levels: intra-agent (individual reasoning uncertainty), inter-agent (interactive uncertainty), and system-level (output uncertainty). Empirical analysis across several benchmarks reveals that our proposed uncertainty quantification reliably indicates system failures, which demonstrates the validity of using them as diagnostic metrics to indicate the system failure. Subsequently, we propose a mitigation strategy by formulating an uncertainty-driven policy optimization to penalize self-contradiction, peer conflict, and low-confidence outputs in a dynamic debating environment. Experiments demonstrate that our proposed uncertainty-driven mitigation reliably calibrates the multi-agent system by consistently improving decision accuracy while reducing system disagreement.

Language models are increasingly used to reason over content they were not trained on, such as new documents, evolving knowledge, and user-specific data. A common approach is retrieval-augmented generation (RAG), which stores verbatim documents externally (as chunks) and retrieves only a relevant subset at inference time for an LLM to reason over. However, this results in inefficient usage of test-time compute (LLM repeatedly reasons over the same documents); moreover, chunk retrieval can inject irrelevant context that increases unsupported generation. We propose a human-like non-parametric continual learning framework, where the base model remains fixed, and learning occurs by integrating each new experience into an external semantic memory state that accumulates and consolidates itself continually. We present PANINI, which realizes this by representing documents as Generative Semantic Workspaces (GSW)—an entity- and event-aware network of question–answer (QA) pairs, sufficient for an LLM to reconstruct the experienced situations and mine latent knowledge via reasoning-grounded inference chains on the network. Given a query, PANINI only traverses the continually-updated GSW (not the verbatim documents or chunks), and retrieves the most likely inference chains. Across six QA benchmarks, PANINI achieves the highest average performance, 5%–7% higher than other competitive baselines, while using 2–30× fewer answer-context tokens, supports fully open-source pipelines, and reduces unsupported answers on curated unanswerable queries. The results show that efficient and accurate structuring of experiences at write time—as achieved by the GSW framework—yields both efficiency and reliability gains at read time. Code is available at https://github.com/roychowdhuryresearch/gsw-memory.

The rapid rise of synthetic media has made deepfake detection a critical challenge for online safety and trust. Progress remains constrained by the scarcity of large, high-quality datasets. Although multimodal large language models (LLMs) exhibit strong reasoning capabilities, their performance on deepfake detection is poor, often producing explanations that are misaligned with visual evidence or hallucinatory. To address this limitation, we introduce a reasoning-annotated dataset for deepfake detection and propose Paragraph-level Relative Policy Optimization (PRPO), a reinforcement learning algorithm that aligns LLM reasoning with image content at the paragraph level. Experiments show that PRPO improves detection accuracy by a wide margin and achieves the highest reasoning score of 4.55/5.0. Ablation studies further demonstrate that PRPO significantly outperforms GRPO under test-time conditions. These results underscore the importance of grounding multimodal reasoning in visual evidence to enable more reliable and interpretable deepfake detection.