ICML 2026 Papers

What does it mean to understand the world? Is it simply to predict future video frames? Developmental cognitive science suggests that understanding the world is fundamentally the process of constructing internal theories of how it works rather than mere prediction, even before language is acquired. However, in machine learning, it remains unclear how to endow AI systems with such theory-building capability from raw, non-textual observation alone. In this paper, we introduce Learning-to-Theorize (L2T), a learning paradigm in which an AI system acquires the ability to construct theories represented as executable programs directly from observation alone. To instantiate this paradigm, we propose the Neural Language-of-Thought Programmer, a neural model that induces and executes latent programs as explanations rather than task-specific predictors or policies. In experiments, we show that this formulation enables explanation-driven generalization, allowing observations to be understood in terms of the programs that generate them.

LLM-based deep research agents are largely built on the ReAct framework. This linear design makes it difficult to revisit earlier states, branch into alternative search directions, or maintain global awareness under long contexts, often leading to local optima, redundant exploration, and inefficient search. We propose Re-TRAC, an agentic framework that performs cross-trajectory exploration by generating a structured state representation after each trajectory to summarize evidence, uncertainties, failures, and future plans, and conditioning subsequent trajectories on this state representation. This enables iterative reflection and globally informed planning, reframing research as a progressive process. Empirical results show that Re-TRAC consistently outperforms ReAct by 15–20% on BrowseComp with frontier LLMs. For smaller models, we introduce Re-TRAC-aware supervised fine-tuning, achieving state-of-the-art performance at comparable scales. Notably, Re-TRAC shows a monotonic reduction in tool calls and token usage across rounds, indicating progressively targeted exploration driven by cross-trajectory reflection rather than redundant search.

Test-time compute scaling allocates inference computation uniformly, uses fixed sampling strategies, and applies verification only for reranking. In contrast, we propose a verifier-guided adaptive framework treating reasoning as iterative trajectory generation and selection. For each problem, the agent runs multiple inference iterations. In each iteration, it optionally produces a high-level plan, selects a set of reasoning tools and a compute strategy together with an exploration parameter, and then generates a candidate reasoning trajectory. A process reward model (PRM) serves as a unified control signal: within each iteration, step-level PRM scores are aggregated to guide pruning and expansion during generation, and across iterations, aggregated trajectory rewards are used to select the final response. Across datasets, our dynamic, PRM-guided approach consistently outperforms direct test-time scaling, yielding large gains on MATH-500 and several-fold improvements on harder benchmarks such as AIME24 and AMO-Bench. We characterize efficiency using theoretical FLOPs and a compute intensity metric penalizing wasted generation and tool overhead, demonstrating that verification-guided allocation concentrates computation on high-utility reasoning paths.

Cooperative reasoning under incomplete information remains complex for both humans and multi-agent AI, requiring agents to transcend individual logic in favor of recursive Theory-of-Mind (ToM) and strategic coordination. To investigate these challenges, we conduct a large-scale evaluation of 17 state-of-the-art LLMs (4B–600B+) on Hanabi card game across 2–5 players. To examine their limitations, we analyze the impact of context engineering and scaffold robustness, ranging from minimal prompts (Watson setting) to Bayesian-motivated scaffolding (Sherlock setting) and multi-turn working memory (Mycroft setting). Our findings reveal that: (1) top-performing models can autonomously track game states via internal working memory, although not reliably, and (2) cross-play performance scales smoothly with model capability. However, even the best models (scoring ≈ 15/25) trail specialist human experts (> 20/25). We introduce and release two novel datasets: HanabiLogs (1,520 annotated trajectories) and HanabiRewards (560 games with dense move-level utilities). By fine-tuning a 4B open-weight model (Qwen3-Instruct) on our datasets, we achieve performance gains of up to 156%, bringing performance to within 3 points of a strong proprietary reasoning model (o4-mini) and surpassing the best non-reasoning model (GPT-4.1) by 52%. Crucially, our HanabiRewards RL-finetuned model further generalizes beyond Hanabi, improving performance on a cooperative group-guessing benchmark by 11 percentage points, temporal reasoning on EventQA by 6.4 points, instruction-following on IFBench by 1.7 Pass@10, and matching AIME 2025 mathematical reasoning Pass@10. Code and datasets are available at https://app.primeintellect.ai/dashboard/environments/mahesh-ramesh/hanabi.

Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that are difficult to detect and correct. In contrast, formal theorem proving provides rigorous, verifiable mathematical reasoning, where each inference step is checked by a trusted compiler, but lacks the exploratory freedom of informal problem-solving. This mismatch leaves current LLM-based math agents without a principled way to combine the strengths of both paradigms. In this work, we introduce Hermes, the first tool-assisted agent that explicitly interleaves informal reasoning with formally verified proofs in Lean. The framework performs intermediate formal checking to prevent reasoning drift and a memory module for proof continuity across multi-step reasoning chains, enabling both exploration and verification. We evaluate Hermes on four challenging mathematical reasoning benchmarks using LLMs of varying parameter scales, from small models to state-of-the-art systems. Across all settings, Hermes reliably improves the reasoning accuracy of base models while substantially reducing reasoning token usage and computational cost compared to reward-based approaches. On difficult datasets such as AIME and HARDMath2, Hermes@1 achieves up to a 40% accuracy improvement while using 80% fewer total inference FLOPs. When scaled at test time, Hermes@5 boosts accuracy further by 20%.

Recently, the physics reasoning capabilities of (M)LLMs have attracted growing attention. However, existing physics benchmarks lack systematic coverage of recent physics Olympiads and direct comparison with human contestants. We present **HiPhO**, the first benchmark dedicated to high school physics Olympiads with human-aligned evaluation. HiPhO highlights three key innovations. **(1) Comprehensive data:** it compiles 13 latest Olympiads from 2024--2025, covering international and regional competitions and spanning mixed modalities from text-only to diagram-based problems. **(2) Professional evaluation:** it adopts official rubrics for fine-grained answer- and step-level grading aligned with human examiners. **(3) Human-level comparison:** it assigns gold, silver, and bronze medals to models based on official medal scores, enabling direct comparison with human contestants. Evaluating 30 (M)LLMs across 13 exams, we find that most open-source MLLMs remain at or below the bronze level, open-source LLMs demonstrate notable progress with multiple gold medals, and closed-source MLLMs achieve 6-13 gold medals, while most models still fall well short of full marks. These results underscore the substantial gap between current (M)LLMs and top human contestants, as well as the room for further improvement. The dataset and leaderboard are available at https://huggingface.co/datasets/SciYu/HiPhO and https://phyarena.github.io, respectively.

We study how reasoning evolves in a language model -- from supervised fine-tuning (SFT) to reinforcement learning (RL) -- by analyzing how a set of theoretically-inspired datasets impacts language model performance in chess. We find that fine-tuning a model to directly predict the best move leads to effective RL and the strongest downstream performance -- however, the RL stage elicits \textit{unfaithful} reasoning (reasoning inconsistent with the chosen move). Alternatively, training on multi-move trajectories yields comparable downstream performance with faithful reasoning and more stable RL. We show that RL induces a substantial positive shift in the distribution of move quality and reduces hallucination rates as a side effect. Finally, we find several SFT-checkpoint metrics -- metrics spanning evaluation performance, hallucination rates, and reasoning quality -- to be predictive of post-RL model performance. We release checkpoints and final models as well as training data, evaluations, and code that allowed us to surpass leading open-source reasoning models in chess with a 7B-parameter model.

Token-level adaptive computation seeks to reduce inference cost by allocating more computation to harder tokens and less to easier ones. However, prior work is primarily evaluated on natural-language benchmarks using task-level metrics, where token-level difficulty is unobservable and confounded with architectural factors, making it unclear whether compute allocation truly aligns with underlying complexity. We address this gap through three contributions. First, we introduce a complexity-controlled evaluation paradigm using existing algorithmic and synthetic language tasks with parameterized difficulty, enabling direct testing of token-level compute allocation. Second, we propose ANIRA, a unified recurrent Transformer framework that supports per-token variable-depth computation while isolating compute allocation decisions from other model factors. Third, we use this framework to conduct a systematic analysis of token-level adaptive computation across alignment with complexity, generalization, and decision timing. Our results show that compute allocation aligned with task complexity can emerge without explicit difficulty supervision, but such alignment does not imply algorithmic generalization: models fail to extrapolate to unseen input sizes despite allocating additional computation. We further find that early compute decisions rely on static structural cues, whereas online halting more closely tracks algorithmic execution state. Code: https://github.com/merlresearch/ANIRA

Scaling test-time compute via long Chain-of-Thought unlocks remarkable gains in reasoning capabilities, yet it faces practical limits due to the linear growth of KV cache and quadratic attention complexity. In this paper, we introduce AccordionThinking, an end-to-end framework where LLMs learn to self-regulate the granularity of the reasoning steps through dynamic summarization. This mechanism enables a Fold inference mode, where the model periodically summarizes its thought process and discards former thoughts to reduce dependency on historical tokens. We apply reinforcement learning to incentivize this capability further, uncovering a critical insight: the accuracy gap between the highly efficient Fold mode and the exhaustive Unfold mode progressively narrows and eventually vanishes over the course of training. This phenomenon demonstrates that the model learns to encode essential reasoning information into compact summaries, achieving effective compression of the reasoning context. Our AccordionThinker demonstrates that with learned self-compression, LLMs can tackle complex reasoning tasks with minimal dependency token overhead without compromising solution quality, and it achieves a 3× throughput while maintaining accuracy on a 48GB GPU memory configuration, while the structured step summaries provide a human-readable account of the reasoning process.

It is widely recognized that reinforcement learning (RL) fine-tuning of large language models often leads to \textit{diversity collapse}, where outputs lack variety. Prior work has proposed a range of heuristics to counteract this effect, but these methods are ad hoc: they frequently trade off correctness for diversity, their effectiveness varies across tasks, and in some cases they even contradict one another. In this work, we place these observations on a rigorous foundation. We first provide a formal proof of why RL fine-tuning exhibits diversity collapse via a selection and reinforcement bias. Next, we make a key observation that any reward modification to address diversity collapse only needs to be applied on the correct trajectories. Building directly on this analysis, we introduce a principled method---\textit{differential smoothing}---that provably improves both correctness and diversity, outperforming vanilla RL as well as widely used entropy-based heuristics. Our theory precisely characterizes when existing heuristics help and why they fail, while showing that differential smoothing is universally superior. Extensive experiments with models from 1B to 7B parameters, across domains including CountDown and real-world mathematical reasoning, demonstrate consistent gains. Differential smoothing improves both Pass@1 and Pass@k, with up to 6.7\% improvements on AIME24 dataset.

Multi-Hop Fact Verification requires complex reasoning across disparate evidence, posing significant challenges for Large Language Models , which may suffer from hallucinations and fractured logical chains. Existing methods, while improving transparency via Chain-of-Thought , often lack explicit modeling of the structural dependencies between evidence and claims. In this work, we introduce an SCM-inspired framework that grounds reasoning in explicit directed dependency graphs, treating verification as a constructive structural reasoning process rather than full causal inference with interventions or counterfactual semantics. We empirically identify an ``inverted U-shaped'' correlation between reasoning-chain length and accuracy, revealing that excessive structural complexity can degrade performance. To address this, we propose a rule-based reinforcement learning strategy using Group Relative Policy Optimization. This approach dynamically optimizes the trade-off between structural depth and conciseness. Extensive experiments on HoVer and EX-FEVER demonstrate that our SCM-GRPO framework outperforms strong baselines while producing more traceable reasoning structures for complex fact verification.

Grading in large undergraduate STEM courses often yields minimal feedback due to heavy instructional workloads. We present a large-scale empirical study of AI grading on real, handwritten single-variable calculus work from the University of California, Irvine. Using OCR-conditioned large language models with structured, rubric-guided prompting, our system produces scores and formative feedback for thousands of handwritten, in-person proctored free-response quiz submissions from nearly 800 students included in the paper’s empirical analysis. In a setting with no single ground-truth label, we evaluate performance against official teaching-assistant grades, student surveys, and independent human review, finding strong alignment with TA scoring and a large majority of AI-generated feedback rated correct or acceptable across quizzes. Beyond calculus, this setting highlights core challenges in OCR-conditioned mathematical reasoning and partial-credit assessment. We analyze key failure modes, propose practical rubric- and prompt-design principles, and introduce a multi-perspective evaluation protocol for reliable real-course deployment. Building on the dataset and evaluation framework developed here, we outline a path toward a future standardized benchmark for AI grading of handwritten mathematics to support reproducible evaluation, transparent comparison, reliable deployment, and future research.

Reinforcement learning with verifiable rewards can improve LLM reasoning, but learning remains sample-inefficient when terminal rewards are sparse. This has motivated a growing line of work on RL with textual feedback, where a critic model generates natural language feedback to guide a reasoning model (the actor), augmenting scalar rewards with richer learning signals. However, existing methods typically treat feedback as fixed or auxiliary, which misses a key property: feedback should not merely be correct, but should improve the policy (actor model) when provided in context. This motivates a paradigm of \textit{learnable textual feedback for RL}. Yet the learnability and usefulness of feedback depend on the policy's ability to learn from it, making RL with learnable feedback an inherently bilevel problem. We formalize this coupling as a Stackelberg bilevel program and derive \emph{Bilevel Natural Language Actor-Critic} (Bi-NAC), which jointly trains a critic to generate reward-improving feedback and an actor to exploit it. Across MATH-500, MBPP, and GPQA, Bi-NAC improves sample and parameter efficiency over RL and fixed-critic baselines: our 2B model outperforms the 3B GRPO baseline, achieving 46.6% versus 41.4% on MATH-500, while our 6B model surpasses the 7B GRPO baseline, achieving 49.3% versus 43.6% on GPQA. Our code is available at [GitHub Repository](https://github.com/sid-in-the-loop/Bi-Natural-Language-Actor-Critic/).

Chain-of-thought (CoT) reasoning and its variants have substantially improved the performance of language models on complex reasoning tasks, yet the precise mechanisms by which different strategies facilitate generalization remain poorly understood. While current explanations often point to increased test-time computation or structural guidance, establishing a consistent, quantifiable link between these factors and generalization remains challenging. In this work, we identify *intrinsic dimensionality* as a quantitative measure for characterizing the effectiveness of reasoning chains. Intrinsic dimensionality quantifies the minimum number of model dimensions needed to reach a given accuracy threshold on a given task. By keeping the model architecture fixed and varying the task formulation through different reasoning strategies, we demonstrate that effective reasoning strategies consistently reduce the intrinsic dimensionality of the task. Validating this on GSM8K with Gemma-3 1B and 4B, we observe a strong inverse correlation between the intrinsic dimensionality of a reasoning strategy and its generalization performance on both in-distribution and out-of-distribution data. Our findings suggest that effective reasoning chains facilitate learning by better compressing the task using fewer parameters, offering a new quantitative metric for analyzing reasoning processes.

Reinforcement learning enhances the reasoning capabilities of large language models but often involves high computational costs due to rollout-intensive optimization. Online prompt selection presents a plausible solution by prioritizing informative prompts to improve training efficiency. However, current methods either depend on costly, exact evaluations or construct prompt-specific predictive models lacking generalization across prompts. This study introduces Generalizable Predictive Prompt Selection (GPS), which performs Bayesian inference towards prompt difficulty using a lightweight generative model trained on the shared optimization history. Intermediate-difficulty prioritization and history-anchored diversity are incorporated into the batch acquisition principle to select informative prompt batches. The small predictive model also generalizes at test-time for efficient computational allocation. Experiments across varied reasoning benchmarks indicate GPS's substantial improvements in training efficiency, final performance, and test-time efficiency over superior baseline methods. The code is available at https://github.com/thu-rllab/GPS.

Identifying and estimating causal relationships from data is a crucial component of empirical research. While large language model-powered tools have shown potential for assisting research workflows, their ability to perform end-to-end causal inference remains underexplored. We introduce CauSciBench, a benchmark that puts LLM-powered tools to the test on causality- driven research questions. Unlike previous related benchmarks that focus on coding alone, CauSciBench enables evaluation across the full pipeline of causal inference: from method and variable selection to computation of causal effects and statistical interpretation in the context of real-world research problems. We evaluated 7 frontier models on over 300 queries derived from scientific publications, textbook problems, sem- inal datasets, and synthetic scenarios. Results show that models consistently perform worse on real datasets, with the key bottleneck being the selection of an appropriate causal inference method.

Given a question, a language model (LM) implicitly encodes a distribution over possible answers. In practice, post-training procedures for LMs often collapse this distribution onto a single dominant mode. While this is generally not a problem for benchmark-style evaluations that assume one correct answer, many real-world tasks inherently involve multiple valid answers or irreducible uncertainty. Examples include medical diagnosis, ambiguous question answering, and settings with incomplete information. In these cases, we would like LMs to generate multiple plausible hypotheses, ideally with confidence estimates for each one, and without computationally intensive repeated sampling to generate non-modal answers. This paper describes a multi-answer reinforcement learning approach for training LMs to perform distributional reasoning over multiple answers during inference. We modify the RL objective to enable models to explicitly generate multiple candidate answers in a single forward pass, internalizing aspects of inference-time search into the model's generative process. Across question-answering, medical diagnostic, and coding benchmarks, we observe improved diversity, coverage, and set-level calibration scores compared to single answer trained baselines. Models trained with our approach require fewer tokens to generate multiple answers than competing approaches. On coding tasks, they are also substantially more accurate. These results position multi-answer RL as a principled and compute-efficient alternative to inference-time scaling procedures such as best-of-k.

Reinforcement Learning with Verifiable Reward (RLVR) is a powerful method for enhancing the reasoning abilities of Large Language Models, but its full potential is limited by a lack of exploration in two key areas: \textbf{Depth} (the difficulty of problems) and \textbf{Breadth} (the number of training instances). Our analysis of the popular GRPO algorithm reveals a bias that down-weights difficult, low-accuracy problems, which are crucial for improving reasoning skills. To address this, we introduce Difficulty Adaptive Rollout Sampling (DARS), a method that re-weights difficult problems by using targeted, multi-stage rollouts. This approach increases the number of rollout outcomes for these harder problems according to our proposed re-balancing schedules and leads to consistent gains in \textit{Pass@K}. We also found that simply enlarging the rollout size isn't effective and can even harm performance. We also investigated the role of breadth by scaling the batch size and using full-batch updates. This significantly improved \textit{Pass@1} performance by maintaining high token-level entropy, which indicates continued exploration and reduced gradient noise. Finally, we present DARS-Breadth, a combined approach that uses DARS with a large breadth of training data. This method demonstrates simultaneous gains in both \textit{Pass@K} and \textit{Pass@1}, confirming that depth (adaptive exploration) and breadth (scaling the training data) are orthogonal and essential dimensions for unlocking the full reasoning power of RLVR.

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4\% and 14.2\%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.