ICLR 2026 论文列表

Reinforcement learning (RL) training of large language models (LLMs) is limited by the policy's ability to generate rollouts with non-zero rewards: without such rewards, the policy is not updated and learning is stalled on hard problems, which are problems that the policy consistently fails to sample any correct rollouts for. We find that many hard problems remain unsolved due to the repeated generation of incorrect intermediate steps in a long reasoning trace; identifying and fixing these requires performing better \emph{credit assignment}. But existing approaches for credit assignment are either impractical or impose a substantial data-writing burden on oracles (\textit{e.g.}, humans). In this paper, we introduce \textbf{Interventional Training} (InT), a framework that leverages single-step oracle interventions to improve LLM reasoning. Given a reasoning attempt and ground-truth answer, the oracle detects and then provides language feedback on a single intermediate reasoning step, which is much cheaper than obtaining a full reasoning trace. \methodname{} then \emph{patches} the LLM by running supervised fine-tuning on the on-policy rollout up to the error, followed by the correction from the oracle. RL on this patched model now generates counterfactual traces and with merely $\approx$$100$ interventions from the oracle, \methodname{} solves 16\% more hard test problems that were previously unsolved (only zero rewards) and also improves performance across multiple standard evals.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts (LoT), the first landscape visualization tool to inspect the reasoning trajectories with certain reasoning methods on any multi-choice dataset. We represent the textual states in a trajectory as numerical features that quantify the states' distances to the answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt LoT to a model that predicts the property they observe. We showcase this advantage by adapting LoT to a lightweight verifier that evaluates the correctness of trajectories. Empirically, this verifier boosts the reasoning accuracy and the test-time scaling effect.

Large Language Models have shown impressive generative capabilities across diverse tasks, but their safety remains a critical concern. Existing post-training alignment methods, such as SFT and RLHF, reduce harmful outputs yet leave LLMs vulnerable to jailbreak attacks, especially advanced optimization-based ones. Recent system-2 approaches enhance safety by adding inference-time reasoning, where models assess potential risks before producing responses. However, we find these methods fail against powerful out-of-distribution jailbreaks, such as AutoDAN-Turbo and Adversarial Reasoning, which conceal malicious goals behind seemingly benign prompts. We observe that all jailbreaks ultimately aim to embed a core malicious intent, suggesting that extracting this intent is key to defense. To this end, we propose ARMOR, which introduces a structured three-step reasoning pipeline: (1) analyze jailbreak strategies from an external, updatable strategy library, (2) extract the core intent, and (3) apply policy-based safety verification. We further develop ARMOR-Think, which decouples safety reasoning from general reasoning to improve both robustness and utility. Evaluations on advanced optimization-based jailbreaks and safety benchmarks show that ARMOR achieves state-of-the-art safety performance, with an average harmful rate of 0.002 and an attack success rate of 0.06 against advanced optimization-based jailbreaks, far below other reasoning-based models. Moreover, ARMOR demonstrates strong generalization to unseen jailbreak strategies, reducing their success rate to zero. These highlight ARMOR’s effectiveness in defending against OOD jailbreak attacks, offering a practical path toward secure and reliable LLMs.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a key paradigm for post-training Large Language Models (LLMs), particularly for complex reasoning tasks. However, vanilla RLVR training has been shown to improve Pass@1 performance at the expense of policy entropy, leading to reduced generation diversity and limiting the Pass@k performance, which typically represents the upper bound of LLM reasoning capability. In this paper, we systematically analyze the policy's generation diversity from the perspective of training problems and find that augmenting and updating training problems helps mitigate entropy collapse during training. Based on these observations, we propose an online Self-play with Variational problem Synthesis (SvS) strategy for RLVR training, which uses the policy's correct solutions to synthesize variational problems while ensuring their reference answers remain identical to the originals. This self-improving strategy effectively maintains policy entropy during training and substantially improves Pass@k compared with standard RLVR, sustaining prolonged improvements and achieving absolute gains of 18.3% and 22.8% in Pass@32 performance on the competition-level AIME24 and AIME25 benchmarks. Experiments on 12 reasoning benchmarks across varying model sizes from 3B to 32B consistently demonstrate the generalizability and robustness of SvS.

Engineering design operates through hierarchical abstraction from system specifications to component implementations, requiring visual understanding coupled with mathematical reasoning at each level. While Multi-modal Large Language Models (MLLMs) excel at natural image tasks, their ability to extract mathematical models from technical diagrams remains unexplored. We present \textbf{CircuitSense}, a comprehensive benchmark evaluating circuit understanding across this hierarchy through 8,006+ problems spanning component-level schematics to system-level block diagrams. Our benchmark uniquely examines the complete engineering workflow: Perception, Analysis, and Design, with a particular emphasis on the critical but underexplored capability of deriving symbolic equations from visual inputs. We introduce a hierarchical synthetic generation pipeline consisting of a grid-based schematic generator and a block diagram generator with auto-derived symbolic equation labels. Comprehensive evaluation of eight state-of-the-art MLLMs, including both closed-source and open-source models, reveals fundamental limitations in visual-to-mathematical reasoning. Closed-source models achieve over 85\% accuracy on perception tasks involving component recognition and topology identification, yet their performance on symbolic derivation and analytical reasoning falls below 19\%, exposing a critical gap between visual parsing and symbolic reasoning. Models with stronger symbolic reasoning capabilities consistently achieve higher design task accuracy, confirming the fundamental role of mathematical understanding in circuit synthesis and establishing symbolic reasoning as the key metric for engineering competence. Our synthetic pipeline code is available at \href{https://anonymous.4open.science/r/CircuitSense-8AC7/README.md}{URL}.

The prevailing paradigm for enhancing the reasoning abilities of Large Language Models (LLMs) revolves around post-training on high-quality, reasoning-intensive data. While emerging literature suggests that reasoning data is increasingly incorporated also during the mid-training stage---a practice that is relatively more proprietary and less openly characterized---the role of such data in pretraining remains unclear. In particular, due to the opaqueness of pretraining corpora in most frontier models, the effect of reasoning data introduced at different phases of pre- and/or post-training is relatively less reported in the scientific literature. This raises several important but unsettled questions: Is adding reasoning data earlier during pre-training any better than introducing it during post-training, when the token counts are controlled? Could earlier inclusion risk overfitting and harm generalization, or instead establish durable foundations that later fine-tuning cannot recover? To address these questions, we conduct the first systematic study of how reasoning data—varying in scale, diversity, and quality—affects LLM performance when introduced at different stages of training. Our findings reveal that front-loading reasoning data into pretraining is critical (19% average gain), establishing foundational capabilities that cannot be fully replicated by later-stage SFT, even with more data. We uncover an asymmetric principle for optimal data allocation: pretraining benefits most from broad diversity in reasoning patterns (11% average gain), while SFT is more sensitive to data quality (15% average gain with high quality data). Furthermore, we show that high-quality pretraining data has latent effects, activated only after SFT, and that naively scaling SFT data can be detrimental, washing away the benefits of early reasoning injection. Collectively, our results challenge the conventional separation of language modeling and reasoning, providing a principled guide for strategically allocating data across the entire training pipeline to build more capable models.

We tackle the 2-norm (Euclidean) k-Hyperplane Clustering problem (k-HC2), which asks for finding k hyperplanes that minimize the sum of squared 2-norm (Euclidean) distances between each point and its closest hyperplane. We solve the problem to global optimality via spatial branch-and-bound techniques (SBB) by strengthening a mixed integer quadratically-constrained quadratic programming formulation with constraints that arise when formulating the problem in p-norms with p ̸= 2. In particular, we show that, for every (appropriately scaled) p ∈ N ∪ {∞}, one obtains a variant of k-HC2 whose optimal solutions yield lower bounds within a multiplicative approximation factor. We focus on the case of polyhedral norms where p = 1, ∞ (which admit a disjunctive-programming reformulation), and prove that strengthening the original formulation by including, on top of the original 2-norm constraints, the constraints of one of the polyhedral-norms leads to an SBB method where nonzero lower bounds are obtained in a linear (as opposed to exponential) number of SBB nodes. Experimentally, we show that our strengthened formulations lead to speedups from 41 to 1.5 orders of magnitude, drastically improving the problem’s solvability to global optimality.

Mathematical reasoning in real-world video presents a fundamentally different challenge than static images or text. It requires interpreting fine-grained visual information, accurately reading handwritten or digital text, and integrating spoken cues, often dispersed non-linearly over time. In such multimodal contexts, success hinges not just on perception, but on selectively identifying and integrating the right details from a rich and noisy stream of content. To this end, we introduce VideoMathQA, a benchmark designed to evaluate whether models can perform such temporally extended cross-modal reasoning on videos. The benchmark spans 10 diverse mathematical domains, covering videos from 10 seconds to over 1 hour. We employ graduate-level experts to ensure high quality, for over 920 man-hours of annotation. To reflect real-world scenarios, questions are designed around three core reasoning challenges: direct problem solving, conceptual transfer, which requires applying learned methods to new problems; and deep instructional comprehension, involving multi-step reasoning over extended explanations and partially worked-out solutions. Each question includes multi-step reasoning annotations, enabling fine-grained diagnosis of model capabilities. Through this benchmark, we establish an evaluation framework for models that must reason, rather than merely perceive, jointly ground concepts across visual, audio, and textual modalities, across temporally extended mathematical problem settings.

While Large Language Models (LLMs) have demonstrated impressive capabilities, their output quality remains inconsistent across various application scenarios, making it difficult to identify trustworthy responses, especially in complex tasks requiring multi-step reasoning. In this paper, we propose a **Tok**en-level **U**ncertainty estimation framework for **R**easoning (**TokUR**) that enables LLMs to self-assess and self-improve their responses in mathematical reasoning. Specifically, we introduce low-rank random weight perturbation during LLM decoding to generate predictive distributions for token-level uncertainty estimation, and we aggregate these uncertainty quantities to capture the semantic uncertainty of generated responses. Experiments on mathematical reasoning datasets of varying difficulty demonstrate that TokUR exhibits a strong correlation with answer correctness and model robustness, and the uncertainty signals produced by TokUR can be leveraged to enhance the model’s reasoning performance at test time. These results highlight the effectiveness of TokUR as a principled and scalable approach for improving the reliability and interpretability of LLMs in challenging reasoning tasks.

Using Reinforcement Learning with Verifiable Rewards (RLVR) to optimize Large Language Models (LLMs) can be conceptualized as progressively editing a query's 'Reasoning Tree'. This process involves exploring nodes (tokens) and dynamically modifying the model's policy at each node. When combined with data scheduling, this process yields further gains in data efficiency and accuracy. However, existing RLVR data scheduling methods typically rely on path-based metrics to rank queries, overlooking the reasoning tree structures of these queries. In this paper, we introduce a novel metric, namely **Reasoning Score (r-score)**, which measures the query's learning difficulty based on the structure of its reasoning tree. Based on the r-score, we propose the **Reasoning Tree Schedule (Re-Schedule)**, a scheduling algorithm that constructs a curriculum progressing from structurally simple (high r-score) to complex (low r-score) queries. Experiments on six math-reasoning benchmarks show that Re-Schedule significantly improves average accuracy, achieving gains of up to 3.2\%. These strong results validate our approach and demonstrate that a structural understanding of the reasoning tree provides a more powerful and principled foundation for RLVR data scheduling.

Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods either focus on theorem-only NL-to-FL auto-formalization or on FL proof synthesis from FL theorems. In practice, auto-formalization of both theorem and proof still requires human intervention, as seen in AlphaProof’s silver-medal performance at the 2024 IMO, where problem statements were manually translated before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem-proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. Our training ensures that NL-FL theorems (and their proofs) are mapped close together in this space if and only if the NL-FL pairs are semantically equivalent. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean’s type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

Motion planning in complex environments remains a core challenge for autonomous driving. While existing rule-based or imitation learning-based motion planning methods perform well in common scenarios, they often struggle with complex, long-tail scenarios. To address this problem, we introduce the Bird's-eye-view Informed Reasoning Driver (BIRDriver), a hierarchical framework that combines a Vision-Language Model (VLM) with a motion planner. BIRDriver leverages the commonsense reasoning capabilities of the VLM to effectively handle these challenging long-tail scenarios. Unlike prior methods that require domain-specific encoders and costly alignment, our approach compresses the environment into a single-frame bird's-eye-view (BEV) map, a paradigm that enables the model to fully leverage its knowledge from internet-scale pre-training. It then generates high-level key points, which are encoded and passed to the motion planner to produce the final trajectory. However, a major challenge is that standard VLMs struggle to generate the precise numerical coordinates required for such key points. We address this limitation by fine-tuning them on a composite dataset of three auxiliary types to enhance spatial localization, scene understanding, and key-point generation, complemented by a token-level weighted mechanism for improved numerical precision. Experiments on the nuPlan dataset demonstrate that BIRDriver outperforms the base motion planner in most cases on both Test14-hard and Test14-random benchmarks, and achieves state-of-the-art (SOTA) performance on the InterPlan long-tail benchmark.

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.

Traditional on-policy Reinforcement Learning with Verifiable Rewards (RLVR) frameworks suffer from experience waste and reward homogeneity, which directly hinders learning efficiency on difficult samples during large language models post-training. In this paper, we introduce Batch Adaptation Policy Optimization (BAPO), an off-policy RLVR framework to improve the data efficiency in large language models post-training. It dynamically selects training batches by re-evaluating historically difficult samples and reusing high-quality ones, while holding a lower bound guarantee for policy improvement. Extensive experiments further demonstrate that BAPO achieves an average 12.5\% improvement over GRPO across mathematics, planning, and visual reasoning tasks. Crucially, BAPO successfully resolves 40.7\% of problems that base models consistently fail to solve.

With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with sufficiently many draws (e.g., $\texttt{pass@1024}$), existing base models already solve nearly all questions on widely used math benchmarks such as MATH-500 and AIME 2024. This suggests that the RL fine-tuning methods prevalent in the LLM reasoning literature largely sharpen existing solution modes rather than discovering entirely new ones. Such sharpening stands in contrast to the broader promise of RL: to foster exploration and to acquire new skills. To move beyond this plateau, we introduce MATH-Beyond (MATH-B), a benchmark deliberately constructed to defeat common open-source models of up to 8B parameters even under large sampling budgets. Improving performance on our benchmark via RL requires methods that learn to reason in ways that go beyond base model capabilities in repeated sampling. Since the problems are drawn from subsets of DAPO-Math-17K and DeepScaleR datasets, they remain topically equivalent to standard high-school math. Validating our premise, RL fine-tuned models such as Nemotron-Research-Reasoning-Qwen-1.5B and DeepScaleR-1.5B-Preview perform poorly on MATH-B at $\texttt{pass@1024}$, showing how existing approaches fall short on tackling harder instances. We hope MATH-B will catalyze exploration-driven RL approaches that elicit deeper reasoning capabilities.

Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories: neural-based and symbolic-based methods, both of which exhibit limitations in reliability and interpretability. To address this challenge, we propose AutoGPS, a neuro-symbolic collaborative framework that solves geometry problems with concise, reliable, and human-interpretable reasoning processes. Specifically, AutoGPS employs a Multimodal Problem Formalizer (MPF) and a Deductive Symbolic Reasoner (DSR). The MPF utilizes neural cross-modal comprehension to translate geometry problems into structured formal language representations, with feedback from DSR collaboratively. The DSR takes the formalization as input and formulates geometry problem solving as a hypergraph expansion task, executing mathematically rigorous and reliable derivation to produce minimal and human-readable stepwise solutions. Extensive experimental evaluations demonstrate that AutoGPS achieves state-of-the-art performance on benchmark datasets. Furthermore, human stepwise-reasoning evaluation confirms AutoGPS's impressive reliability and interpretability, with 99\% stepwise logical coherence.

Large reasoning models (LRMs) excel at a long chain of reasoning but often fail to faithfully follow instructions regarding output format, constraints, or specific requirements. We investigate whether this gap can be closed by integrating an instruction-tuned model (ITM) into an LRM. Analyzing their differences in parameter space, namely task vectors, we find that their principal subspaces are nearly orthogonal across key modules, suggesting a lightweight merging with minimal interference. However, we also demonstrate that naïve merges are fragile because they overlook the output format mismatch between LRMs (with explicit *thinking* and *response* segments) and ITMs (answers-only). We introduce **RAIN-Merging** (Reasoning-Aware Instruction-attention guided Null-space projection Merging), a gradient-free method that integrates instruction following while preserving thinking format and reasoning performance. First, with a small reasoning calibration set, we project the ITM task vector onto the null space of forward features at thinking special tokens, which preserves the LRM's structured reasoning mechanisms. Second, using a small instruction calibration set, we estimate instruction attention to derive module-specific scaling that amplifies instruction-relevant components and suppresses leakage. Across four instruction-following benchmarks and nine reasoning & general capability benchmarks, RAIN-Merging substantially improves instruction adherence while maintaining reasoning quality. The gains are consistent across model scales and architectures, translating to improved performance in agent settings.

While chain-of-thought prompting enables powerful multi-step reasoning in Large Language Models (LLMs), the stochastic nature of the generation process undermines its reliability. In this work, we first analyze thousands of reasoning paths to identify Reasoning Drift, a key failure mode where models get locked into flawed reasoning patterns. We reveal that the manifestation of drift is a complex interplay between universal functional tendencies and unique, model-specific signatures. Based on the diagnosis, we propose Reasoning-Aware Activation Steering, a novel inference-time intervention method to gently nudge the model's activations away from pathological patterns. We pre-compute a library of vectors from contrastive functional transitions and apply them dynamically. Experiments show that our method effectively mitigates the drift problem and boosts accuracy. Additionally, it generalizes to out-of-distribution tasks, demonstrating a deeper capture of valid reasoning principles.

Training large language models (LLMs) for complex reasoning via Reinforcement Learning with Verifiable Rewards (RLVR) is effective but limited by reliance on costly, domain-specific supervision. We explore Reinforcement Learning from Internal Feedback (RLIF), a framework that enables LLMs to learn from intrinsic signals without external rewards or labeled data. We propose Intuitor, an RLIF method that uses a model's own confidence—termed self-certainty—as its sole reward signal. Intuitor replaces external rewards in Group Relative Policy Optimization (GRPO) with self-certainty scores, enabling fully unsupervised learning. Experiments demonstrate that Intuitor matches GRPO's performance on mathematical benchmarks and achieves competitive, sometimes better, generalization to out-of-domain tasks like code generation, without requiring gold solutions or test cases. Our findings show that intrinsic model signals can drive effective learning across domains, offering a scalable alternative to RLVR for autonomous AI systems where verifiable rewards are unavailable. Code is available in the supplementary materials.