ICML 2026 Papers

Recent research on reasoning models explores the meta-awareness of language models, including their ability to determine optimal thinking duration, recognize knowledge boundaries, and structure concept-level thinking. While current large reasoning models depend solely on answer-based verification, we show that adding meta-awareness objectives leads to significant performance gains over models without such meta-knowledge. **MAPR** utilizes a self-generated task of predicting rollout statistics - specifically length, pass-rate, and concepts used - allowing for verification against the actual statistics. Furthermore, by leveraging this self-predictive capability, the model can regulate its reasoning behavior by i) filtering out trivial or unsolvable prompts, ii) reducing lengthy generations that tend to be incorrect, and iii) generating hints relevant to the problem. The results are inspiring: **MAPR** yields significant improvements in both accuracy and training efficiency on various reasoning benchmarks. More specifically, our method can speed up GRPO training by over 1.28$\times$ to reach the same performance, and achieve 83.18\% gain in accuracy on AIME25, and a 13.04\% average gain over six mathematics benchmarks.

Current chemical large language models (LLMs) predominantly rely on explicit Chain-of-Thought (CoT) to solve complex reasoning problems. However, forcing nonverbal tacit chemical logic into discrete natural language imposes a fundamental ``modality mismatch,'' creating an artificial bottleneck for reasoning. We introduce LatentChem, a reasoning interface that decouples chemical logic from linguistic generation, enabling the model to process information via continuous thought vectors and dynamic perception. Our investigation reveals a pivotal emergent behavior: spontaneous internalization, defined here as self-selected under outcome-only optimization. When optimized for task success, the model abandons verbose textual derivations in favor of implicit latent computation, suggesting that it identifies the continuous manifold as a more native substrate for chemical logic. This paradigm shift also proves to be a superior computational strategy: LatentChem achieves a 59.88\% non-tie win rate against the strong CoT baseline on the rigorous ChemCoTBench, while delivering a broad 10.84$\times$ average reduction in reasoning step overhead (5.96$\times$ wall-clock speedup) across all evaluated benchmarks. Our results provide empirical evidence that chemical reasoning is more naturally and effectively realized as continuous latent dynamics rather than discretized linguistic trajectories.

Compressing long chains of thought (CoT) into compact latent tokens is crucial for efficient reasoning with large language models (LLMs). Recent studies employ autoencoders to achieve this by reconstructing textual CoT from latent tokens, thus encoding CoT semantics. However, treating textual CoT as the reconstruction target forces latent tokens to preserve surface-level linguistic features (e.g., word choice and syntax), introducing a strong linguistic inductive bias that prioritizes linguistic form over reasoning structure and limits logical abstraction. Thus, we propose ImgCoT that replaces the reconstruction target from textual CoT to the visual CoT obtained by rendering CoT into images. This substitutes linguistic bias with spatial inductive bias, i.e., a tendency to model spatial layouts of the reasoning steps in visual CoT, enabling latent tokens to better capture global reasoning structure. Moreover, although visual latent tokens encode abstract reasoning structure, they may blur reasoning details. We thus propose a loose ImgCoT, a hybrid reasoning that augments visual latent tokens with a few key textual reasoning steps, selected based on low token log-likelihood. This design allows LLMs to retain both global reasoning structure and fine-grained reasoning details with fewer tokens than the complete CoT. Extensive experiments across multiple datasets and LLMs demonstrate the effectiveness of the two versions of ImgCoT.

While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically principled early stopping methods that monitor uncertainty signals during generation to mitigate this issue. Our first approach is nonparametric and provides finite-sample guarantees on the probability of halting too early on well-posed queries. Our second approach is parametric: it models inter-arrival times of uncertainty keywords as a renewal process and applies sequential testing for stopping. We conduct empirical evaluations on reasoning tasks across several domains and models. Our results indicate that uncertainty-aware early stopping can improve both efficiency and reliability in LLM reasoning. The performance varies across domains, and we observe especially significant gains for math reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a prevailing paradigm for enhancing reasoning in Multimodal Large Language Models (MLLMs). However, relying solely on outcome supervision risks reward hacking, where models learn spurious reasoning patterns to satisfy final answer checks. While recent rubric-based approaches offer fine-grained supervision signals, they suffer from high computational costs of instance-level generation and inefficient training dynamics caused by treating all rubrics as equally learnable. In this paper, we propose **Stratified Rubric-based Curriculum Learning (RuCL)**, a novel framework that reformulates curriculum learning by shifting the focus from data selection to reward design. RuCL generates generalized rubrics for broad applicability and stratifies them based on model competence, dynamically adjusting their weights to guide the model from foundational perception to advanced logical reasoning. Extensive experiments on various visual reasoning benchmarks show that RuCL yields a remarkable **+7.83%** average improvement over the Qwen2.5-VL-7B model, achieving a state-of-the-art accuracy of **60.06%**.

Reinforcement learning (RL) post-training is a dominant approach for improving the reasoning performance of large language models (LLMs), yet growing evidence suggests that its gains arise primarily from distribution sharpening rather than the acquisition of new capabilities. Recent work has shown that sampling from the power distribution of LLMs using Markov chain Monte Carlo (MCMC) can recover performance comparable to RL post-training without relying on external rewards; however, the high computational cost of MCMC makes such approaches impractical for widespread adoption. In this work, we propose a theoretically grounded alternative that eliminates the need for iterative MCMC. We derive a novel formulation showing that the global power distribution can be approximated by a token-level scaled low-temperature one, where the scaling factor captures future trajectory quality. Leveraging this insight, we introduce a training-free and verifier-free algorithm that sharpens the base model's generative distribution autoregressively. Empirically, we evaluate our method on math, QA, and code tasks, and show that our method matches or surpasses one-shot GRPO without relying on any external rewards, while reducing inference latency by over $10\times$ compared to MCMC-based sampling.

Prompt optimization is critical for maximizing the performance of large language models (LLMs). However, it often relies on costly labeled data. Self-supervised methods reduce data dependency, but they suffer from optimization ambiguity or high computational costs. To address these limitations, we propose the Meta-Reasoning Prompt Engineering Agent (MR.PEA), a self-supervised prompt optimization framework that operates with minimal input. MR.PEA leverages meta-reasoning to iteratively build task-specific knowledge, including problem-solving strategies and evaluation criteria, while adaptively retrieving external information to enhance its understanding. This knowledge guides the generation of diverse validation examples, targeted prompt refinement, and comprehensive quality assessments. Experiments on GSM8K and Big-Bench Hard show that MR.PEA outperforms existing baselines, achieving an average performance gain of 7.4% with an optimization cost as low as $0.01 per task.

Large reasoning models (LRMs) like OpenAI o1 and DeepSeek-R1 achieve high accuracy on complex tasks by adopting long chain-of-thought (CoT) reasoning paths. However, the inherent verbosity of these processes frequently results in redundancy and overthinking. To address this issue, existing works leverage Group Relative Policy Optimization (GRPO) to reduce LRM output length, but their static length-reward designs fail to adapt to problem difficulty and response-length distributions, causing over-compression and compromised accuracy. Therefore, we propose *SmartThinker*, a novel GRPO-based efficient reasoning method with progressive CoT length calibration. *SmartThinker* makes a two-fold contribution: First, it dynamically estimates the optimal length with peak accuracy during training and guides overlong responses toward it to reduce reasoning length while sustaining accuracy. Second, it dynamically modulates the length-reward coefficient to avoid the unwarranted penalization of correct reasoning paths. Extensive experimental results show that *SmartThinker* achieves up to 52.6\% length compression with improved accuracy and achieves up to 16.6\% accuracy relative improvement on challenging benchmarks like AIME25. The source code can be found at https://github.com/SJTU-RTEAS/SmartThinker.

Large reasoning models (LRMs) achieve remarkable reasoning performance by generating long chains-of-thought (CoT). However, standard supervised fine-tuning (SFT) treats all tokens uniformly, indiscriminately minimizing loss across both essential reasoning steps and those that are noisy, redundant, or instance-specific. This often leads student models to memorize superficial patterns rather than acquire generalizable reasoning capabilities. To better understand this limitation, we introduce \textit{Loss Subspace Attribution}, a gradient decomposition analysis approach that uncovers a striking geometric structure: Gradients corresponding to effective reasoning predominantly lie within a low-rank consensus subspace, while conflicting or unstructured signals dominate the residual subspace. Guided by this insight, we propose \textbf{\textit{Spectral-guided Learning}}, a step-level distillation strategy that uses spectral strength to identify reasoning steps aligned with the consensus subspace and prioritizes their contribution to parameter updates, while suppressing gradients from the residual subspace. Experiments across various LRMs and diverse complex reasoning tasks consistently demonstrate that focusing optimization on the consensus subspace yields more robust and generalizable student models.

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. By effectively balancing exploration and exploitation, ePF significantly outperforms strong baselines on challenging math benchmarks, achieving up to a 50% relative improvement in task reward.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing RLVR methods typically rely on on-policy optimization from scratch, resulting in high sampling costs and inefficient utilization of accumulated experience. As model capabilities and policy behaviors evolve during training, recent attempts to reuse experience via fixed reasoning trajectories further suffer from policy mismatch. Motivated by these limitations, we argue that experience in RLVR should not be reused as fixed reasoning trajectories, but instead expressed in a policy-adaptive manner. In this work, we propose Experience-Augmented Policy Optimization (EAPO), which leverages a prior RL-optimized policy as an action-level experience prior and selectively injects experience at critical decision points during rollout. To ensure stable and unbiased learning from experience-augmented rollouts, EAPO further incorporates an adapted importance sampling scheme. Experiments on using Qwen-2.5-math 7b and Qwen-3-8B on five different benchmarks demonstrate that EAPO consistently improves reasoning performance over state-of-the-art RLVR methods.

Mathematical search problems present a unique challenge for Reinforcement Learning (RL) due to vast search spaces and sparse rewards. In previous works, the Andrews-Curtis (AC) conjecture was established as an illustrative example of such problems. In this work, we identify a critical structural barrier in the AC landscape: a "Two Hump" distribution, where problem instances are either trivially solvable or effectively impossible, with a scarcity of intermediate "hard-but-solvable" instances required for effective learning. We tackle this challenge through two primary avenues: novel data generation techniques to populate the difficulty gap, and significant algorithmic enhancements including the introduction of supermoves and Transformer-based architectures. We demonstrate substantial performance improvements over previous baselines, and release new comprehensive benchmark datasets including **AC-19** (125,192 AC-trivial presentations of varying difficulty with length at most 19) and **AC-1M** (1,136,154 hard AC-trivial presentations of length at most 30), the first large-scale, publicly available datasets of this kind.

Although recent tool-augmented benchmarks involve complex requests, evaluation remains limited to answer matching, neglecting critical trajectory aspects like efficiency, hallucination, and adaptivity. The most straightforward method for evaluation is to compare an agent’s trajectory with the ground-truth, but annotating all valid ground-truth trajectories is prohibitively expensive. In this manner, we introduce TRACE, a reference free framework for the multi-dimensional evaluation of tool-augmented LLMs. By incorporating an evidence bank which accumulates knowledge from preceding steps, TRACE assesses an agent’s reasoning trajectory effectively. To validate our framework, we develop a new meta-evaluation dataset with diverse and flawed trajectories, each labeled with multi-faceted performance scores. Our results confirm that TRACE accurately evaluates complex trajectories even with small open source LLMs. Furthermore, we apply our method to evaluate the trajectories that agents produce while solving tool-augmented tasks, presenting previously unreported observations and their corresponding insights.

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal “overthinking,” leading to performance degradation. In this work, we quantify inference-time effort by identifying *deep-thinking tokens*—tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that *deep-thinking ratio* (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@$n$, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@$n$ matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Recent advances in large language models (LLMs) have demonstrated that reinforcement fine-tuning of pretrained base models can lead to significant gains in reasoning performance at inference time. In this work, we theoretically analyze why reinforcement fine-tuning induces better reasoning ability than purely supervised fine-tuning (SFT) methods. We model chain-of-thought (CoT) reasoning as a pathfinding problem on graphs and compare the popular method of reinforcement learning with verifiable rewards (RLVR) against traditional SFT. We prove that SFT, when trained on golden shortest paths without negative examples, fails to learn how to efficiently backtrack. In contrast, an RLVR-trained model can learn how to efficiently backtrack from dead ends using only outcome reward. This leads to a provable inference-time compute separation between the two methods, and demonstrates that RLVR allows the model to learn the location of difficult decisions in a reasoning chain, ultimately allowing for better allocation of inference-time compute. Finally, we show that the reasoning traces of an RLVR model can be distilled to train a base model to backtrack efficiently as well.

Neural networks adapt through first-order parameter updates, yet it remains unclear whether such updates preserve logical coherence. We investigate the geometric limits of the Linear Propagation Assumption (LPA), the premise that local updates coherently propagate to logical consequences. To formalize this, we adopt relation algebra and study three core operations on relations: negation flips truth values, converse swaps argument order, and composition chains relations. For negation and converse, we prove that guaranteeing direction-agnostic first-order propagation necessitates a tensor factorization separating entity-pair context from relation content. However, for composition, we identify a fundamental obstruction. We show that composition reduces to conjunction, and prove that any conjunction well-defined on linear features must be bilinear. Since bilinearity is incompatible with negation, this forces the feature map to collapse. These results suggest that failures in knowledge editing, the reversal curse, and multi-hop reasoning may stem from common structural limitations inherent to the LPA.

Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial SOS representation, which directly proves the target inequality, and we further certify the proof in Lean, yielding an end-to-end pipeline from heuristic discovery to machine-checked proof. Experiments on challenging benchmarks involving polynomials with up to 10 variables demonstrate the effectiveness and scalability of the proposed method.

Theory of Mind (ToM) is a must-acquire skill for modern foundation model systems to operate effectively and safely in the real world. Recent works have explored honing ToM via post-training; however, we show that such progress is confounded by a pervasive “shortcut” issue: tasks can reach up to 99% accuracy by simply exploiting spurious causal correlations, leading to a false sense of ToM. Motivated by this, we first develop a framework to systematically examine ToM datasets for shortcuts and provide guidance for future development. We find that questions reducible to pure state tracking, such as “belief,” are especially shortcut-prone compared to mind questions, such as “intention,” where reasoning beyond tracking is required. Using four shortcut-free datasets across three ToM contexts, we then comprehensively study whether Reinforcement Fine-Tuning with verifiable rewards and explicit reasoning chains, called Thinking-RFT, elevates ToM beyond Supervised Fine-Tuning, or SFT. Our key findings are as follows. First, Thinking-RFT effectively improves ToM in all scenarios, with a 6% improvement over SFT, particularly in complex higher-order reasoning, with a 10% improvement over SFT, and multimodal cases, with a 7% improvement over SFT. It also generalizes notably better to unseen domains and higher-order queries while being more robust to counterfactuals. Second, ToM benefits specifically from the joint effect of reasoning and RL: Thinking-RFT outperforms No-Thinking-RFT by 7% on average. Third, RFT works by learning to ground its reasoning on anchor cues, such as keywords and state changes, that correspond to causal factors. We believe our study is useful for developing effective and robust ToM post-training datasets and advancing critical ToM capabilities. Project code is available at: https://github.com/jkz-338/Robust-ToM-RL.git

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data toward a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn serves as a stepping stone to efficiently learn rare long-tailed skills. Our results offer an alternative perspective on what constitutes an effective data distribution for training models.