ICLR 2026 Papers

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which substantially increases computational cost and response latency. While existing methods incorporate length rewards to GRPO to promote concise reasoning, they incur significant performance degradation. We identify the root cause: when rewards for correct but long rollouts are penalized, GRPO's group-relative advantage function can assign them negative advantages, actively discouraging valid reasoning. To overcome this, we propose Decoupled Reward Policy Optimization (DRPO), a novel framework that decouples the length-based learning signal of correct rollouts from incorrect ones. DRPO ensures that reward signals for correct rollouts are normalized solely within the positive group, shielding them from interference by negative samples. The DRPO's objective is grounded in integrating an optimized positive data distribution, which maximizes length-based rewards under a KL regularization, into a discriminative objective. We derive a closed-form solution for this distribution, enabling efficient computation of the objective and its gradients using only on-policy data and importance weighting. Of independent interest, this formulation is general and can incorporate other preference rewards of positive data beyond length. Experiments on mathematical reasoning tasks demonstrate DRPO's significant superiority over six efficient reasoning baselines. Notably, with a 1.5B model, our method achieves 77\% length reduction with only 1.1\% performance loss on simple questions like GSM8k dataset, while the follow-up baseline sacrifices 4.3\% for 68\% length reduction.

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically verified. Formal theorem proving systems such as Lean 4 offer automated verification with complete accuracy, motivating recent efforts to build specialized prover LLMs that generate verifiable proofs in formal languages. However, a significant gap remains: current prover LLMs solve substantially fewer problems than general-purpose LLMs operating in natural language. We introduce Hilbert, an agentic framework that bridges this gap by combining the complementary strengths of informal reasoning and formal verification. Our system orchestrates four components: an informal LLM that excels at mathematical reasoning, a specialized prover LLM optimized for Lean 4 tactics, a formal verifier, and a semantic theorem retriever. Given a problem that the prover is unable to solve, Hilbert employs recursive decomposition to split the problem into subgoals that it solves with the prover or reasoner LLM. It leverages verifier feedback to refine incorrect proofs as necessary. Experimental results demonstrate that Hilbert, substantially outperforms existing approaches on key benchmarks, achieving 99.2\% on miniF2F, 6.6\% points above the best publicly available method. Hilbert achieves the **best known result** on PutnamBench. It solves 462/660 problems (70.0\%), outperforming proprietary approaches like SeedProver (50.4\%) and achieving a 422\% improvement over the best publicly available baseline. Thus, Hilbert effectively narrows the gap between informal reasoning and formal proof generation.

The prevailing approach to distilling reasoning from Large Language Models (LLMs)—behavioral cloning from textual rationales—is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the underlying algorithmic structure of thought, resulting in a critical lack of logical robustness. We argue that instead of cloning text, distillation should transfer this algorithmic structure directly. We introduce Reasoning Scaffolding, a framework that reframes reasoning as a structured generation process. Our method first abstracts the teacher's thought process into a sequence of discrete, interpretable semantic signals (e.g., Contrast, Addition) that act as a scaffold. The student model is then trained via a multi-task objective to both (1) predict the next semantic signal, anticipating the reasoning flow, and (2) generate the corresponding step, conditioned on that signal. This multi-task scheme acts as a powerful regularizer, compelling the student to internalize the computational patterns of coherent reasoning. On a suite of challenging reasoning benchmarks, our method significantly outperforms state-of-the-art distillation in both accuracy and logical consistency, providing a path towards creating smaller models that are genuine reasoners, not just fluent mimics.

Reasoning distillation, a cost-effective approach for enhancing student model performance, has attracted increasing attention. It typically leverages a large teacher model to generate reasoning paths, which are then used to fine-tune a student model so that it mimics the teacher's behavior in training contexts. However, previous approaches have lacked a detailed analysis of the origins of the distilled model's capabilities. It remains unclear whether the student can maintain consistent behaviors with the teacher in novel test-time contexts, or whether it regresses to its original output patterns, raising concerns about the generalization of distillation models. To analyse this question, we introduce a cross-model Reasoning Distillation Provenance Tracing framework. For each action (e.g., a sentence) produced by the distilled model, we obtain the predictive probabilities assigned by the teacher, the original student, and the distilled model under the same context. By comparing these probabilities, we classify each action into four categories: (i) teacher-originated actions, (ii) student-originated actions, (iii) pre-existing actions in both models not enhanced by distillation, and (iv) pre-existing actions boosted through distillation. By systematically disentangling the provenance of each action, we experimentally demonstrate that, in test-time contexts, the distilled model can indeed generate teacher-originated actions, which correlate with and plausibly explain observed performance on distilled model. Building on this analysis, we further propose a teacher-guided data selection method. Unlike prior approach that rely on heuristics (e.g., selecting data most aligned with the student's original distribution), our method directly compares teacher–student divergences on the training data, providing a principled selection criterion. We validate the effectiveness of our approach across multiple representative teacher models (Deepseek-R1-671B, QwQ-32B, GPT-OSS-120B) and diverse student models (Qwen2.5-7B-Instruct, Qwen4-4B-Base, Qwen3-8B-Base, Qwen3-4B-Instruct-2507). The results highlight the utility of our provenance-tracing framework and underscore its promise for reasoning distillation. We hope to share Reasoning Distillation Provenance Tracing, along with our insights into reasoning distillation, with the community.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases—thinking and solution—with independently allocated budgets. At test time, Elastic Reasoning prioritizes the completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale. Code is available in the supplementary material.

Large language models (LLMs) have achieved significant advancements in reasoning capabilities through reinforcement learning (RL) via environmental exploration. As the intrinsic properties of the environment determine the abilities that LLMs can learn, the environment plays a important role in the RL finetuning process. An ideal LLM reasoning environment should possess three core characteristics: scalability, generalizable reasoning, and verifiability. However, existing mathematical and coding environments are difficult to scale due to heavy reliance on expert annotation, while the skills learned in game-based environments are too specialized to generalize. To bridge this gap, we introduce the \textbf{S}tructured \textbf{I}n-context \textbf{E}nvironment (SIE) framework. SIE achieves scalability by automatically constructing reasoning environments from large-scale structured data, where the rich compositional patterns naturally support generalizable reasoning. Moreover, the explicit schemas and reasoning chains in structured data provide a foundation for rule-based verifiability. Experimental results show that SIE framework not only achieves substantial improvements in in-domain structured reasoning, but also enables the learned compositional reasoning skills to generalize effectively to out-of-domain mathematical and logical reasoning tasks. We further explored learning in information-limited partial SIEs and found that LLMs can infer the missing information through exploring the environment, leading to robust reasoning improvements and generalization performance. Our code can be available at \url{https://anonymous.4open.science/r/SIE_ICLR-EE6F}

In this paper, we claim that 3D visual grounding is the cornerstone of spatial reasoning and introduce the $\textit{Grounded-Spatial Reasoner (GS-Reasoner)}$ to explore the effective spatial representations that bridge the gap between them. Existing 3D LLMs suffer from the absence of a unified 3D representation capable of jointly capturing semantic and geometric information. This deficiency is manifested either in poor performance on grounding or in an excessive reliance on external modules, ultimately hindering the seamless integration of grounding and spatial reasoning. To address this, we propose a simple yet effective \emph{dual-path pooling} mechanism that tightly aligns geometric features with both semantic and positional cues, constructing a unified image patch-based 3D representation that encapsulates all essential information without extra tokens. Leveraging this holistic representation, GS-Reasoner is the first 3D LLMs that achieves autoregressive grounding entirely without external modules while delivering performance comparable to state-of-the-art models, establishing a unified and self-contained framework for 3D spatial reasoning. To further bridge grounding and spatial reasoning, we introduce the $\textit{Grounded Chain-of-Thought (GCoT)}$ dataset. This dataset is meticulously curated to include both 3D bounding box annotations for objects referenced in reasoning questions and step-by-step reasoning paths that integrate grounding as a core component of the problem-solving process. Extensive experiments demonstrate that GS-Reasoner achieves impressive results on 3D visual grounding, which in turn significantly enhances its spatial reasoning capabilities, leading to state-of-the-art performance.

Large Language Models (LLMs) have achieved impressive performance on complex tasks by generating human-like, step-by-step rationales, referred to as \textit{reasoning trajectory}, before arriving at final answers. However, the length of these reasoning trajectories often far exceeds that of the final answers, which incurs substantial inference costs even for relatively simple tasks. Advanced methods typically attempt to compress reasoning trajectory length through post-training, but they remain decoding-intensive and fail to inherently mitigate the efficiency challenge. In this work, we challenge the necessity of generating full reasoning trajectories and empirically demonstrate that LLMs can generate accurate answers using only fragmental reasoning paths, without relying on complete token-by-token sequences. To this end, we propose a novel \textbf{Latent Reasoning Tuning (LRT)} framework, which empowers LLMs to perform reasoning using implicit, compact, learnable representations instead of explicit textual trajectories. Technically, LRT replaces the costly autoregressive generation of reasoning steps with a single forward pass through a lightweight reasoning network, which generates latent vectors that encapsulate the necessary reasoning logic and condition the LLM to produce the final answer. Experiments on mathematical and out-of-domain benchmarks demonstrate that our LRT consistently outperforms relevant efficient reasoning methods. Moreover, by transforming explicit reasoning into latent reasoning, our approach surpasses the state-of-the-art Qwen3 hybrid reasoning framework.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs’ reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyper-parameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce ***C****onditional adv****AN****tage estimati****ON*** (***CANON***), amplifying the impact of the target metric without presuming its direction. Specifically, *CANON* regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, *CANON* based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, *CANON* further improves token efficiency, yielding a more favorable Pareto frontier in the performance–cost trade-off.

Frontier language models appear strong at solving reasoning problems, but their performance is often inflated by shortcuts such as memorisation and knowledge. We introduce LingOLY-TOO, a challenging reasoning benchmark of 6,995 questions that counters these shortcuts by applying expert-designed obfuscations to Linguistics Olympiad problems. These obfuscations preserve the underlying solution logic while removing orthographic clues that could trigger patterns from memorisation or knowledge. Our experiments show that models exploit shortcuts on the original questions as performance markedly drop upon obfuscation. Even the best reasoning models remain highly sensitive, with scores dropping from around $0.60$ on original problems to $0.48$ after obfuscation. LingOLY-TOO disentangles reasoning from knowledge, offering a clear measure of true reasoning capabilities.

Recent advances in large language models (LLMs) show strong promise for formal reasoning. However, most LLM-based theorem provers remain constrained by the need for expert-written formal statements as inputs, limiting their applicability to real-world problems expressed in natural language. We address this gap by focusing on autoformalization, the task of translating informal problems into formal statements. We propose Mathesis, the first pipeline for the systematic study of formal theorem proving from natural language. It contributes the first autoformalizer trained with reinforcement learning, which integrates syntactic, semantic, and prover feedback as reward signals to yield accurate and verifiable formalizations. This is further supported by our novel LeanScorer framework for evaluating semantic correctness. To assess real-world applicability, we introduce Gaokao-Formal, a benchmark of 495 complex proof problems from the college entrance exams. Experiments demonstrate that our autoformalizer improves pass rates by 45% on Gaokao-Formal and 6% on MiniF2F compared to state-of-the-art baselines. Paired with provers, our autoformalizer consistently enhances proving accuracy, including a 42% gain for DeepSeek-Prover-V2 on Gaokao-Formal. Our code is available at https://anonymous.4open.science/r/Mathesis-2D14.

Reasoning language models have demonstrated remarkable performance on many challenging tasks in math, science, and coding. Choosing the right reasoning model for practical deployment involves a performance and cost tradeoff at two key levels: model size and reasoning budget, where larger models and higher reasoning budget lead to better performance but with increased cost and latency. In this work, we tackle this tradeoff from the angle of model configuration routing for different queries, and present RADAR (Reasoning–Ability and Difficulty-Aware Routing), a lightweight, interpretable, and scalable routing framework. Inspired by psychometrics, RADAR learns an item response model from model responses with different budgets to different queries, with interpretable parameters including query difficulties and model-budget abilities. RADAR then routes queries with higher difficulty to model-budget pairs with higher ability, and vice versa. We conduct extensive experiments on 8 widely used challenging reasoning benchmarks, demonstrating the superior performance of RADAR compared to state-of-the-art model routing methods. RADAR also exhibits query generalization capabilities, showing strong performance on out-of-distribution queries in all benchmarks. RADAR is also scalable and can efficiently integrate additional models, by dynamically selecting a small set of evaluation queries to estimate their abilities.

Large Reasoning Models (LRMs) achieve strong reasoning performance by generating long chains of thought (CoTs), yet only a small fraction of these traces meaningfully contributes to answer prediction, while the majority contains repetitive or truncated content. Such output redundancy is further propagated after supervised finetuning (SFT), as models learn to imitate verbose but uninformative patterns, which can degrade performance. To this end, we incorporate integrated gradient attribution to quantify each token's influence on final answers and aggregate them into two segment-level metrics: (1) \textit{attribution strength} measures the overall attribution magnitude; and (2) \textit{direction consistency} captures whether tokens' attributions within a segment are uniformly positive or negative (high consistency), or a mixture of both (moderate consistency). Based on these two metrics, we propose a segment-level selective learning framework to identify important segments with high attribution strength but moderate consistency that indicate reflective rather than shallow reasoning. The framework then applies selective SFT on these important segments while masking loss for unimportant ones. Experiments across multiple models and datasets show that our approach improves accuracy and output efficiency, enabling more effective learning from long reasoning traces.

Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent to their parallelism remain largely unexplored. To this end, we characterize what types of reasoning problems MDMs can provably solve and how efficiently. We do this by connecting MDMs to the well-understood reasoning frameworks of chain of thought (CoT) and padded looped transformers (PLTs) in the finite-precision log-width setting: We show that MDMs and polynomially-padded PLTs are, in fact, equivalent in this setting, and that MDMs can solve all problems that CoT-augmented transformers can. Moreover, we showcase classes of problems (including regular languages) for which MDMs are inherently more efficient than CoT transformers, where parallel generation allows for substantially faster reasoning.

Large language models (LLMs) have achieved remarkable performance across diverse reasoning tasks, yet their deployment is hindered by prohibitive computational and memory costs. Quantization-aware training (QAT) enables ultra-low-bit compression (<4 bits per weight), but existing QAT methods often degrade reasoning capability, partly because complex knowledge structures are introduced during the post-training process in LLMs. In this paper, through a systematic investigation of how quantization affects different data domains, we find that its impact on pre-training and reasoning capabilities differs. Building on this insight, we propose a novel two-stage QAT pipeline specifically designed for reasoning LLMs. In the first stage, we quantize the model using mixed-domain calibration data to preserve essential capabilities across domains; in the second stage, we fine-tune the quantized model with a teacher-guided reward-rectification loss to restore reasoning capability. We first demonstrate that mixed-domain calibration outperforms single-domain calibration by up to 2.74% improvement on average over six tasks, including reasoning and pre-trained tasks. Following experiments on five reasoning benchmarks show that our 2-bit-quantized Qwen3-8B outperforms post-training quantization (PTQ) baselines by 50.45% on average. Moreover, compared to ultra-low-bit-specialized models such as BitNet-2B4T, our pipeline achieves about 2% higher mathematical-reasoning accuracy using only 40K training sequences.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language “reasoning chains”, their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or “hallucinate”) in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score—a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations—outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this limitation by enabling large language models (LLMs) to generate soft, abstract tokens, thus facilitating reasoning within a continuous concept space. In this paper, we investigate the $\textit{Soft Thinking}$ capabilities of various LLMs through a systematic analysis of their internal behavior using a suite of probing techniques. Contrary to the prevailing belief that Soft Thinking supports parallel exploration of diverse reasoning paths, our findings reveal that $\textbf{LLMs behave as single-threaded reasoners}$—they predominantly rely on the token with the highest probability in the soft input to predict the next step. This behavior induces a greedy feedback loop that suppresses alternative reasoning paths and undermines the benefits of transmitting richer information via Soft Tokens. To address this $\textit{Greedy Pitfall}$, we propose $\textbf{Stochastic Soft Thinking}$, which introduces stochasticity to break free from the greedy tendency. Our experiments demonstrate that incorporating $\textit{randomness}$—particularly with the $\textbf{Gumbel-Softmax trick}$—can alleviate the limitations of vanilla approaches and unleash the potential of Soft Thinking, resulting in superior performance across eight reasoning benchmarks.

Recent frontier models employ long-chain-of-thought reasoning to explore solution spaces in context and achieve stronger performance. While many works study distillation to build smaller yet capable models, most focus on English and little is known about language-specific reasoning. To bridge this gap, we first introduce **Language-Mixed CoT**, a reasoning schema that switches between English and a target language, using English as an anchor to excel in reasoning while minimizing translation artifacts. As a Korean case study, we curate **Yi-Sang-HQ**: 5.79M native-Korean prompts from web Q&A, exams, STEM, and code; 3.7M long reasoning traces generated from Qwen3-32B; and a targeted 260k high-yield subset. We train nine models (4B–35B) across six families (Qwen2.5, Llama-3.1, Gemma-3, etc). Our best model, **KO-REAson-35B**, achieves state-of-the-art performance, with the highest overall average score ($64.0_{\pm2.5}$), ranking first on 5/9 benchmarks and second on the remainder. Smaller and mid-sized models also benefit substantially, with an average improvement of $+18.6$ points across the evaluated nine benchmarks. Ablations show **Language-Mixed CoT** is more effective than monolingual CoT, indicating that reasoning patterns can be engineered to improve non-English performance. We release our data-curation pipeline, evaluation system, datasets, and models to advance research on language-specific reasoning.

Chain-of-Thought (CoT) has emerged as an effective paradigm to enhance the reasoning ability of large language models (LLMs) in complex tasks. However, existing approaches still face two major challenges: (1) the lack of a global mechanism to integrate and interact across diverse reasoning hypotheses, and (2) the absence of structured analysis techniques to filter redundancy and extract salient reasoning features. To address these challenges, we propose GHS-TDA (Global Hypothesis Space with Topological Data Analysis), a two-stage reasoning framework that achieves synergistic enhancement through global information integration and topological feature analysis. Specifically, (i) Global Hypothesis Space (GHS) constructs a semantically enriched global hypothesis graph via agenda-driven multi-agent interactions, integrating diverse hypotheses and their semantic relations; (ii) Topological Data Analysis (TDA) applies persistent homology to extract multi-scale topological features, identify stable connected components and self-consistent loops, and derive a redundancy-free reasoning skeleton chain. GHS-TDA preserves reasoning diversity while leveraging topological stability to achieve self-aware convergence, ultimately producing high-confidence and interpretable reasoning paths. Experimental results show that GHS-TDA consistently outperforms existing methods across multiple benchmark datasets, demonstrating its effectiveness and competitiveness in complex reasoning scenarios.