ICLR 2026 Papers

Recent Large Language Models (LLMs) have made remarkable progress, but they still struggle with complex reasoning tasks such as logical deduction and planning. This is partly because they rely primarily on token-level probability relationships, which limits their ability to reason effectively. In this paper, inspired by cognitive science and neurosymbolic AI, we introduce Structured Reasoning, which aimes at enhancing the reasoning capabilities of LLMs from the step level. To this end, we first collect high‑frequency, domain‑agnostic reasoning step tags and construct a structured reasoning dataset with those tags. Then, we treat a reasoning process as a directed acyclic graph, where the vertices represent steps and the edges indicate the direction of reasoning. In this context, an efficient reasoning process corresponds to, or can be characterized by, a sparse reasoning graph. To construct reasoning graphs, we introduce structured tags for reliable step extraction from LLM outputs. For single-graph optimization, we propose the MaxFlow reward, which rewards graphs with balanced node contributions and fewer redundant steps. The quality of a sparse reasoning graph can be reflected by the total flow from all steps to the final answer. For multi-graph comparison, we propose the LCS reward, which selects reliable reasoning paths by identifying optimal common subsequences (consecutive steps) shared across multiple generated responses (sequences). Experiments with DeepSeek-R1-Distill-Qwen-1.5B and 7B models show that our method consistently outperforms GRPO and other carefully tuned baselines across various context lengths (0.5k–8k). Structured Reasoning shows particular strength in efficiency (better performance with fewer steps) and stability (consistently generating high-quality outputs across a temperature range of 0.1 to 1.0).

We study test-time scaling, where a model improves its answer through multi-round self-reflection at inference. We introduce In-Context Policy Optimization (ICPO), in which an agent optimizes its response in context using self-assessed or externally observed rewards without modifying its parameters. To explain this ICPO process, we theoretically show that with sufficient pretraining under a novel Fisher-weighted logit-matching objective, a single-layer linear self-attention model can provably imitate policy-optimization algorithm for linear bandits. Building on this theory, we propose Minimum-Entropy ICPO (ME-ICPO), a practical algorithm that iteratively uses its response and self-assessed reward to refine its response in-context at inference time. By selecting the responses and their rewards with minimum entropy, ME-ICPO ensures the robustness of the self-assessed rewards via majority voting. Across standard mathematical reasoning tasks, ME-ICPO attains competitive, top-tier performance while keeping inference costs affordable compared with other inference-time algorithms. Overall, ICPO provides a principled understanding of self-reflection in LLMs and yields practical benefits for test-time scaling for mathematical reasoning.

Reasoning Large Language Models (RLLMs) excelling in complex tasks present unique challenges for digital watermarking, as existing methods often disrupt logical coherence or incur high computational costs. Token-based watermarking techniques can corrupt the reasoning flow by applying pseudo-random biases, while semantic-aware approaches improve quality but introduce significant latency or require auxiliary models. This paper introduces ReasonMark, a novel watermarking framework specifically designed for reasoning-intensive LLMs. Our approach decouples generation into an undisturbed Thinking Phase and a watermarked Answering Phase. We propose a Criticality Score to identify semantically pivotal tokens from the reasoning trace, which are distilled into a Principal Semantic Vector (PSV). The PSV then guides a semantically-adaptive mechanism that modulates watermark strength based on token-PSV alignment, ensuring robustness without compromising logical integrity. Extensive experiments show ReasonMark surpasses state-of-the-art methods by reducing text Perplexity by 0.35, increasing translation BLEU score by 0.164, and raising mathematical accuracy by 0.67 points. These advancements are achieved alongside a 0.34% higher watermark detection AUC and stronger robustness to attacks, all with a negligible increase in latency. This work enables the traceable and trustworthy deployment of reasoning LLMs in real-world applications.

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-13% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor’s outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a $9.02\%$ gain on in-domain tasks and a $5.70\%$ gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

Hallucinations in Large Language Models (LLMs) pose a major barrier to their reliable use in critical decision-making. Although existing hallucination detection methods have improved accuracy, they still struggle with disentangling semantic and reasoning information and maintaining robustness. To address these challenges, we propose HARP (Hallucination detection via reasoning subspace projection), a novel hallucination detection framework. HARP establishes that the hidden state space of LLMs can be decomposed into a direct sum of a semantic subspace and a reasoning subspace, where the former encodes linguistic expression and the latter captures internal reasoning processes. Moreover, we demonstrate that the Unembedding layer can disentangle these subspaces, and by applying Singular Value Decomposition (SVD) to its parameters, the basis vectors spanning the semantic and reasoning subspaces are obtained. Finally, HARP projects hidden states onto the basis vectors of the reasoning subspace, and the resulting projections are then used as input features for hallucination detection in LLMs. By using these projections, HARP reduces the dimension of the feature to approximately 5% of the original, filters out most noise, and achieves enhanced robustness. Experiments across multiple datasets show that HARP achieves state-of-the-art hallucination detection performance; in particular, it achieves an AUROC of 92.8% on TriviaQA, outperforming the previous best method by 7.5%.

Evaluation using Large Language Model (LLM) judges has been widely adopted in English and shown to be effective for automatic evaluation. However, their performance does not generalize well to non-English settings, and it remains unclear what constitutes effective multilingual training for such judges. In this paper, we introduce mR3, a massively multilingual, rubric-agnostic reward reasoning model trained on 72 languages, achieving the broadest language coverage in reward modeling to date. We present a comprehensive study of data and curriculum selection for training to identify effective strategies and data sources for building high-quality reward models, including support for reasoning in the target language. Our approach attains state-of-the-art performance on multilingual reward model benchmarks, surpassing much larger models (i.e., GPT-OSS-120B) while being up to 9x smaller, and its effectiveness is further confirmed through extensive ablation studies. Finally, we demonstrate the effectiveness of mR3 in off-policy preference optimization and validate the quality of its reasoning traces and rubric-based evaluations through human studies with 20 annotators across 12 languages, where mR3 models' reasoning is preferred, including for extremely low-resource languages that are entirely unseen during training. Our models, data, and code are available as open source at https://github.com/rubricreward/mr3.

Large language models (LLMs) perform strongly on many language tasks but still struggle with complex multi-step reasoning across disciplines. Existing reasoning datasets often lack disciplinary breadth, reasoning depth, and diversity, as well as guiding principles for question synthesis. We propose DESIGNER: a DESIGN-logic-guidEd Reasoning data synthesis pipeline that leverages naturally available, extensive raw documents to generate multidisciplinary questions. The central insight is the notion of Design Logic, a form of reusable meta-knowledge that encapsulates the structured process human experts use to transform knowledge into complex exam questions, enabling LLMs to generate new questions with the same complex reasoning patterns from entirely different source texts with explicit control over difficulty, diversity, and question types. We use LLMs to reverse-engineer and abstract over 120,000 Design Logics from existing questions across various disciplines. By designing a two-stage retrieve-and-generate mechanism to match these Design Logics with raw corpus, we synthesized two large-scale reasoning datasets that span 75 disciplines: DLR-Book (3.04 million questions from the book corpus) and DLR-Web (1.66 million questions from the web corpus). Data analysis indicates that the questions synthesized by our method exhibit greater difficulty and diversity compared to those in the baseline datasets. Supervised fine-tuning (SFT) on Qwen3 and Llama3 with our data substantially improves multidisciplinary reasoning and outperforms baseline datasets. Notably, by applying SFT on the base versions of these models using only our data, we even surpass their official final models that have undergone the full post-training.

Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models by encouraging step-by-step intermediate reasoning, and recent advances have extended this paradigm to Multimodal Large Language Models (MLLMs). In the medical domain, where diagnostic decisions depend on nuanced visual cues and sequential reasoning, CoT aligns naturally with clinical thinking processes. However, Current benchmarks for medical image understanding generally focus on the final answer while ignoring the reasoning path. An opaque process lacks reliable bases for judgment, making it difficult to assist doctors in diagnosis. To address this gap, we introduce a new M3CoTBench benchmark specifically designed to evaluate the correctness, efficiency, impact, and consistency of CoT reasoning in medical image understanding. M3CoTBench features (1) a diverse, multi-level difficulty dataset covering 24 examination types, (2) 13 varying-difficulty tasks, (3) a suite of CoT-specific evaluation metrics (correctness, efficiency, impact, and consistency) tailored to clinical reasoning, and (4) a performance analysis of multiple MLLMs. M3CoTBench systematically evaluates CoT reasoning across diverse medical imaging tasks, revealing current limitations of MLLMs in generating reliable and clinically interpretable reasoning, and aims to foster the development of transparent, trustworthy, and diagnostically accurate AI systems for healthcare.

Learning causal effects from data is a fundamental and well-studied problem across science, especially when the cause-effect relationship is static in nature. However, causal effect is less explored when there are dynamical dependencies, i.e., when dependencies exist between entities across time. In general, it is not possible to reconstruct the causal graph from data alone. The conventional static causal structure recovery algorithms employ tests such as the Fischer-z test and the chi-square test to assess the conditional independence (CI) of data which forms the basis for recovering Markov Equivalent Graphs (MEGs) wherein causal structure can be recovered partially. For data that are dynamically related, multivariate least square estimation, based on Wiener Filters (WFs) relying on second order statistics for estimating a data stream from other streams, provides a means of recovering influence structures of the directed network underlying the data. Here, WF based projections can be determined in time-domain or in frequency-domain; the question this article sets out to answer is which is better? Here, we obtain concentration bounds on the accuracy of the WF estimation in both time and frequency-based approaches. Exploiting the computation speed of Fast Fourier Transform (FFT), we establish that the frequency domain provides distinct advantages. Moreover, frequency domain projections involve complex numbers; we establish that the phase properties of the resulting estimates can be effectively leveraged for better recovery of the MEG in a large class of networks; the time-domain has no analogue of phase. Thus we report the "Wiener-Phase" algorithm provides the best accuracy as well as computational advantages. We validate the theoretical analysis with numerical results. Performance comparison with state of the art algorithms are also provided. Further, the proposed algorithms are validated on a real field dataset known as the "river-runoff" dataset collected from the online repository of CauseMe, and on measurement data from transistor based circuits.

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Diagrams represent a form of visual language that encodes abstract concepts and relationships through structured symbols and their spatial arrangements. Unlike natural images, they are inherently symbolic, and entirely artificial. They thus pose unique challenges for Multimodal Large Language Models (MLLMs) distinct from natural image processing. Recent studies have shown that MLLMs often exhibit flawed reasoning and hallucinations when handling diagram inputs. We investigate here whether these limitations stem from shortcomings in the models' ability to interpret diagrams themselves. To this end, we develop a diagnostic test suite that isolates perception from reasoning. Our systematic evaluation reveals that MLLMs perform poorly on basic perceptual tasks, e.g., shape classification, object counting, relationship identification, and object grounding, with near-zero accuracy on fine-grained grounding. Further analysis shows that weak diagram perception leads to ``blind faith in text", where models rely on textual shortcuts rather than visual understanding (that is, they are $\textit{Math Blind}$). We hypothesize that enabling models to capture the inherent structural properties of diagrams, represented as graphs of primitives and their interrelationships, is essential for improving diagram understanding. Experiments with 7B and 32B MLLMs validate this assumption, with models trained on such representations achieving a +79\% gain on the grounding task. Crucially, these gains transfer to reasoning, achieving 3–4\% cross-suite improvements on three public benchmarks even without additional chain-of-thought reasoning data. Our findings demonstrate that low-level perception supports faithful high-level reasoning in mathematical MLLMs. We provide both methodological frameworks and empirical evidence to guide future research in this direction. All implementations will be released upon acceptance.

Large Language Models (LLMs) are increasingly applied to chemistry, tackling tasks such as molecular name conversion, captioning, text-guided generation, and property or reaction prediction. A molecule’s properties are fundamentally determined by its composition and structure, encoded in its molecular graph; thus, reasoning about molecular properties requires understanding and reasoning over the molecular structure. Yet, most existing benchmarks emphasize general chemical knowledge, rely on literature or surrogate labels that risk leakage or bias, or reduce evaluation to multiple-choice questions. We introduce MolecularIQ, a molecular structure reasoning benchmark focused exclusively on symbolically verifiable tasks. MolecularIQ spans three orthogonal axes — molecular complexity, multi-task load, and reasoning complexity — covering feature counting, index-based feature attributions, and constrained generation. MolecularIQ enables fine-grained evaluation of reasoning over molecular graphs and produces capability fingerprints that localize model failures to specific tasks and molecular regimes. This provides actionable insights into the strengths and limitations of current chemistry LLMs and guides the development of models that reason faithfully over molecular structure. On MolecularIQ, large MoE models with higher reasoning budgets lead across categories, while chemistry-tuned LLMs underperform their generalist bases, indicating limited transfer from narrow task fine-tuning.

We introduce Music Flamingo, a novel large audio–language model, designed to advance music (including song) understanding in foundational audio models. While audio–language research has progressed rapidly, music remains challenging due to its dynamic, layered, and information-dense nature. Progress has been further limited by the difficulty of scaling open audio understanding models, primarily because of the scarcity of high-quality music data and annotations. As a result, prior models are restricted to producing short, high-level captions, answering only surface-level questions, and showing limited generalization across diverse musical cultures. To address these challenges, we curate MF-Skills, a large-scale dataset labeled through a multi-stage pipeline that yields rich captions and question–answer pairs covering harmony, structure, timbre, lyrics, and cultural context. We fine-tune an enhanced Audio Flamingo 3 backbone on MF-Skills and further strengthen multiple skills relevant to music understanding. To improve the model's reasoning abilities, we introduce a post-training recipe: we first cold-start with MF-Think, a novel chain-of-thought dataset grounded in music theory, followed by GRPO-based reinforcement learning with custom rewards. Music Flamingo achieves state-of-the-art results across 10+ benchmarks for music understanding and reasoning, establishing itself as a generalist and musically intelligent audio–language model. Beyond strong empirical results, Music Flamingo sets a new standard for advanced music understanding by demonstrating how models can move from surface-level recognition toward layered, human-like perception of songs. We believe this work provides both a benchmark and a foundation for the community to build the next generation of models that engage with music as richly and meaningfully as humans do. Demo: https://musicflamingo.github.io

Neural network architectures have made considerable advances in their ability to solve reasoning problems, but many state-of-the-art methods fail at systematic compositional generalization. To address this, we propose a novel architecture which uses a nonparametric latent space, information-theoretic regularization of this space, and test-time gradient-based search to achieve strong performance on OOD compositional meta-learning tasks such as ARC-like program induction, Raven's progressive matrices, and linguistic systematicity tasks. Our proposed architecture, Abduction Transformer, uses nonparametric mixture distributions to represent inferred hidden causes of few-shot meta-learning instances. These representations are refined at test-time via gradient descent to better account for the observed few-shot examples, a form of variational posterior inference which allows Abduction Transformer to solve meta-learning tasks that require novel recombinations of knowledge acquired during training. Our method outperforms standard transformer architectures and previous test-time adaptive approaches, indicating a promising new direction for neural networks capable of systematic generalization.

As AI systems progresses, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks (fail to) predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

Reinforcement Learning with Verifiable Reward (RLVR) effectively solves complex tasks but demands extremely long context lengths during training, leading to substantial computational costs. While multi-stage training can partially mitigate this, starting with overly short contexts often causes irreversible performance degradation, ultimately failing to reduce overall training compute significantly. In this paper, we introduce **T**hinking-**F**ree **P**olicy **I**nitialization (**TFPI**), a simple yet effective adaptation to RLVR that bridges long Chain-of-Thought (CoT) distillation and standard RLVR. TFPI employs a simple *ThinkFree* operation, explicitly discarding the thinking content via a direct *</think>* append, to reduce token usage during inference. Training with *ThinkFree*-adapted inputs improves performance and lowers token consumption, even in the original slow-thinking mode. Extensive experiments across various benchmarks have shown that {\method} accelerates RL convergence, achieves a higher performance ceiling, and yields more token-efficient reasoning models without specialized rewards or complex training designs. With TFPI only, we train a 4B model to reach 89.0% accuracy on AIME24 and 65.5% on LiveCodeBench using less than 4K H20 hours.

Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves translating problems into formal logic and using a logic solver. Although off-the-shelf logic solvers are in principle substantially more efficient than LLMs at logical reasoning, they assume that all relevant facts are provided in a question and are unable to deal with missing commonsense relations. In this work, we propose a novel method that uses feedback from the logic solver to augment a logic problem with commonsense relations provided by the LLM, in an iterative manner. This involves a search procedure through potential commonsense assumptions to maximize the chance of finding useful facts while keeping cost tractable. On a collection of pure-logical reasoning datasets, from which some commonsense information has been removed, our method consistently achieves considerable improvements over existing techniques, demonstrating the value in balancing neural and symbolic elements when working in human contexts.

Large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, excel in contextual reasoning by leveraging extensive world knowledge and deep contextual understanding. However, their high computational costs limit deployment in resource-constrained settings. Conversely, small language models (SLMs) are more computationally efficient but often struggle with contextual reasoning due to limited parameter capacity and challenges like catastrophic forgetting. Existing enhancement methods for SLMs—such as knowledge distillation and data synthesis—still depend on additional training and face inherent limitations. To address this, we propose Navigation, a novel training-free framework that improves SLMs’ contextual reasoning by distilling LLM-derived contextual processing expertise into generalizable navigation templates. These templates, stored in a scalable Navigation database, guide SLMs through a three-stage process—Generation, Utilization, and Update—to locate and process critical information within complex contexts. Experiments demonstrate that our approach yields an average 10.7\% accuracy gain with a template count equivalent to no more than 2.1\% of the dataset size, enabling models such as Qwen2.5-3B-Instruct and Llama-3.2-3B-Instruct to outperform GPT-3.5-Turbo on diverse contextual reasoning tasks.