ICML 2026 论文列表

Solving complex geometric problems inherently requires interleaved reasoning: a tight alternation between constructing diagrams and performing logical deductions. Although recent Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities in visual generation and plotting, we identify a counter-intuitive and underexplored phenomenon. Naively applying Supervised Fine-Tuning (SFT) on interleaved plot–solution data leads to a substantial degradation in reasoning performance compared to text-only baselines. We argue that this failure stems from a fundamental limitation of SFT, which primarily induces distributional alignment: the model learns to reproduce the surface format of interleaved plotting but fails to internalize the causal dependency between the generated plot and reasoning steps. To overcome this limitation, we propose Faire (**F**unctional **a**lignment for **i**nterleaved **re**asoning), a reinforcement learning framework that enforces three casual constraints to move beyond superficial imitation toward functional alignment. Extensive experiments show that Faire induces a qualitative shift in model behavior in which the plotting is effectively internalized, yielding competitive performance on challenging geometric reasoning benchmarks.

When evaluating Large Language Models (LLMs) in question-answering domains, multiple-choice question answering (MCQA) is widely used because it enables automatic grading. However, MCQA also exposes models to answer options that can be exploited in ways that inflate reasoning ability. We study this phenomenon across $15$ question-answering benchmarks and $27$ LLMs by systematically varying how and when models are exposed to answer options. For non-reasoning LLMs, MCQA can remain a good proxy for free-text performance when any chain-of-thought is produced only before the options are revealed. However, this "decoupled" format is not realizable for most reasoning models: they are designed to emit reasoning tokens whenever they are prompted, so if options are present they inevitably "reason over" the options. In practice, this makes reasoning models particularly effective at extracting signal from options, and can create large, misleading gains over free-text baselines. To characterize how models exploit MCQA, we introduce diagnostic probes that isolate option-only and question-plus-option exploitation pathways, and we quantify how design choices such as distractor strength and "none-of-the-above" answers effect exploitability. Finally, we examined the practice of multiple choice as an error diagnostic: inferring a model's mistake from the wrong option it picks. On benchmarks where reasoning can be expressed as code, we ask models to output code, we then executed it varying the inputs, and compared the resulting input–output behavior, revealing failure modes that MCQA diagnostics obscure. Lastly, we offer practical guidelines when analyzing results from MCQA that better reflect LLMs' genuine reasoning capabilities.

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME$^2$ principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code and data are available at https://github.com/Simplified-Reasoning/TRM.

Understanding reasoning in large language models is complicated by evaluations that conflate multiple reasoning types. We isolate analogical reasoning, where a model transfers an attribute between entities that share known properties, and study when such transfer can emerge from training. To make the problem analytically tractable, we study a minimal transformer-style abstraction that isolates how learned representations support analogical reasoning. Within this setting, we prove three key results. First, joint training on similarity and attribution premises enables analogical reasoning through aligned representations. Second, sequential training succeeds only when similarity structure is learned before specific attributes, revealing a curriculum asymmetry. Third, in our stylized setting, two-hop reasoning $(a \to b, b \to c \Rightarrow a \to c)$ can be viewed as analogical reasoning with identity bridges $(b=b)$, which appear explicitly in training data. Together, these results reveal a unified mechanism: entities with shared properties become aligned in representation space, enabling property transfer through feature resemblance. Experiments with architectures up to 8B parameters show qualitative agreement with the theory and suggest that representational geometry plays an important role in analogical reasoning beyond the stylized model.

Supervised fine-tuning with expert demonstrations often produces models that imitate outputs without internalizing the reasoning processes needed for robust generalization. While critique-based approaches show promise, training models to generate critiques directly, such as Critique Fine-Tuning (CFT), can lead to output-format drift and degradation of general capabilities. We propose $\textbf{C}$ritique-$\textbf{G}$uided $\textbf{D}$istillation (CGD), a training framework that decouples critique consumption from critique generation. During fine-tuning, the student is trained to refine flawed responses conditioned on teacher critiques. CGD treats critiques as a $\textit{training-time-only}$ supervision signal, encouraging internalization of error-aware reasoning: critiques guide learning but are absent at inference. Across five model families, CGD consistently outperforms CFT and standard distillation on mathematical reasoning benchmarks, yielding 7\% average improvements and gains of up to +15.0\% on AMC23 and +12.2\% on MATH-500. On challenging competition problems such as AIME24 and AIME25, CGD achieves substantially higher Pass@1 and stronger performance at low Pass@k, indicating improved reasoning quality per sample. Importantly, CGD preserves general instruction-following capabilities where CFT degrades significantly ($-$21.3\% on IFEval). These results position CGD as a practical and compute-efficient intermediate training paradigm for reasoning-centric tasks without introducing architectural inference-time overhead.

Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. However, the mechanisms underlying analogical reasoning in Transformers remain poorly understood. In this work, inspired by the notion of functors in category theory, we formalize analogical reasoning as the inference of correspondences between entities across categories. Based on this formulation, we introduce synthetic tasks that evaluate the emergence of analogical reasoning under controlled settings. We find that the emergence of analogical reasoning is highly sensitive to data characteristics, optimization choices, and model scale. Through mechanistic analysis, we show that analogical reasoning in Transformers decomposes into two key components: (1) geometric alignment of relational structure in the embedding space, and (2) the application of a functor within the Transformer. These mechanisms enable models to transfer relational structure from one category to another, realizing analogy. Finally, we quantify these effects and find that the same trends are observed in pretrained LLMs. In doing so, we move analogy from an abstract cognitive notion to a concrete, mechanistically grounded phenomenon in modern neural networks.

Distilling long-form reasoning from teacher models into smaller students requires selecting which candidate solutions to train on. Recent work argues that one should select responses the student model assigns highest probability, i.e., favoring solutions ``natural'' to the student. However, we find that this approach works within a single teacher but fails when scaling to long reasoning traces from multiple diverse teachers. We identify a key cause: this approach scores entire solutions, but students generalize by recombining familiar reasoning steps, not by memorizing complete solutions. Full-trajectory scoring optimizes the wrong target; it rewards global fluency while the transferable signal lies in local step transitions. We propose Local Average Log Probability (LALP), which scores each reasoning step using only a small window of preceding context, measuring whether each step is justified by its immediate premises rather than whether the full response looks natural to the student. LALP enables two practical use cases: selecting the best teacher before fine-tuning and curating training data from diverse teacher pools. Across math, coding, and science reasoning tasks, LALP consistently improves accuracy when selecting the most natural solutions by a large margin.

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments using math-only data with two widely-used methods: Reinforcement Learning (RL) and Supervised Finetuning (SFT) with detailed ablations. On top of the observation that RL-tuned models transfer better than SFT-tuned models, we identify on-policy fine-tuning as the key mechanism underlying cross-domain transfer, regardless of whether the training signal comes from RL or supervised learning. Latent-space representation and token-space distribution shift analyses reveal that off-policy SFT induces substantial representation and output drift, while on-policy RL preserves general-domain structure. Our results suggest a need to rethink the post-training recipes, particularly the reliance on off-policy SFT-distilled data to advance reasoning models.

Inference-time scaling via chain-of-thought (CoT) reasoning is a major driver of state-of-the-art LLM performance, but it comes with substantial latency and compute costs. We address a fundamental theoretical question: *how many* reasoning tokens are required to solve a problem as input size grows? By extending the bounded attention prefix oracle (BAPO) model--an abstraction of LLMs that quantifies the information flow required to solve a task--we prove lower bounds on the CoT tokens required for three canonical BAPO-hard tasks: binary majority, triplet matching, and graph reachability. We show that each requires $\Omega(n)$ reasoning tokens when the input size is $n$. We complement these results with matching or near-matching upper bounds via explicit constructions. Finally, our experiments with frontier reasoning models show approximately linear reasoning token scaling on these tasks and failures when constrained to smaller reasoning budgets, consistent with our theoretical lower bounds. Together, our results identify fundamental bottlenecks in inference-time compute through CoT and offer a principled tool for analyzing optimal reasoning length.

On-policy reinforcement learning methods like GRPO suffer from \emph{mode collapse}: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (\textbf{D}istribution-\textbf{M}atching \textbf{P}olicy \textbf{O}ptimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group-level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality—an ideal testbed for evaluating exploration. DMPO achieves {43.9\% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1\%)} and {43.1\% on vision-based NP-Bench (vs. 38.4\%)}—demonstrating 9\% and 12\% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0\%) and out-of-domain tasks (+2.3\%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Disease screening is critical for early detection and timely intervention in clinical practice. However, most current screening models for medical images suffer from limited interpretability and suboptimal performance. They often lack effective mechanisms to reference historical cases or provide transparent reasoning pathways. To address these challenges, we introduce EviScreen, an evidential reasoning framework for disease screening that leverages region-level evidence from historical cases. The proposed EviScreen offers retrospection interpretability through regional evidence retrieved from dual knowledge banks. Using this evidential mechanism, the subsequent evidence-aware reasoning module makes predictions using both the current case and evidence from historical cases, thereby enhancing disease screening performance. Furthermore, rather than relying on post-hoc saliency maps, EviScreen enhances localization interpretability by leveraging abnormality maps derived from contrastive retrieval. Our method achieves superior performance on our carefully established benchmarks for real-world disease screening, yielding notably higher specificity at clinical-level recall. Code is publicly available at https://github.com/DopamineLcy/EviScreen.

Large-scale web-harvested datasets have fueled the progress of cross-modal retrieval but inevitably suffer from noisy correspondence, which severely degrades model generalization. Existing methods primarily address this by filtering out noise or seeking a substitute label, yet they predominantly remain bound by a “Discrete Selection” paradigm. We argue that relying on a single discrete proxy induces SinglePoint Fragility and Discretization Error. To overcome these limitations, we propose a novel framework, Intra-modal Neighbor-aware Noise Rectification (IN2R), which shifts the paradigm from searching for a substitute to synthesizing a reliable supervision target. Leveraging the intrinsic geometric stability of intra-modal data, IN2R employs a Graph Refiner to perform relational reasoning over neighbors retrieved from a dynamic Cross-Model Memory. Instead of propagating discrete labels, our method synthesizes a continuous, soft prototype that reflects the consensus of the local semantic neighborhood, effectively rectifying inter-modal misalignment. Extensive experiments on Flickr30K, MS-COCO, and CC152K demonstrate that IN2R significantly outperforms state-of-the-art methods.

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

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.

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.

The Gilbert-Pollak Conjecture, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times that of the Euclidean minimum spanning tree (the Steiner ratio). A sequence of improvements through the 1980s culminated in a lower bound of $0.824$, with no substantial progress reported over the past three decades. Recent advances in LLMs have demonstrated strong performance on contest-level mathematical problems, yet their potential for addressing open, research-level questions remains largely unexplored. In this work, we present a novel AI system for obtaining tighter lower bounds on the Steiner ratio. Rather than directly prompting LLMs to solve the conjecture, we task them with generating rule-constrained geometric lemmas implemented as executable code. These lemmas are then used to construct a collection of specialized functions, which we call verification functions, that yield theoretically certified lower bounds of the Steiner ratio. Through progressive lemma refinement driven by reflection, the system establishes a new certified lower bound of 0.8559 for the Steiner ratio. The entire research effort involves only thousands of LLM calls, demonstrating the strong potential of LLM-based systems for advanced mathematical research.

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.

Retrosynthesis prediction aims to infer the reactant molecules based on a given product molecule, which is a fundamental task in chemical synthesis. However, existing methods rely on a static pattern-matching paradigm, which limits their ability to perform effective logical decision-making from chemical data, leading to a black-box process. We propose Retro-Expert, an interpretable retrosynthesis framework that performs collaborative reasoning by combining the complementary strengths of Large Language Models and specialized models via pure reinforcement learning. It outputs natural language explanations grounded in chemical logic through three components: (1) specialized models provide chemical knowledge that is distilled into a high-quality chemical decision space, (2) LLM-driven critical reasoning to generate predictions with an interpretable reasoning path, and (3) knowledge-grounded policy optimization refines the interpretable decision policy. Experiments show that Retro-Expert surpasses both LLM-based and specialized models across different metrics, while generating chemically grounded explanations that enhance chemists' trust in practice. The source code for this paper is available at https://github.com/MagixRab-ll/Retro-Expert