RL for Language Model Reasoning

RL: Reinforcement Learning

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This field studies how reward feedback can teach language models to solve multi-step problems, use tools, and decide how much reasoning a task needs. A common approach is reinforcement learning from verifiable rewards (RLVR), often using group-relative policy optimization, where sampled solutions are scored for correctness; other methods add step-level rewards, process verifiers, search, or teacher guidance to address sparse feedback. Work also explores curricula, adaptive rollout budgets, self-distillation, and controls for reasoning length and diversity. Key open tensions include balancing exploration with stable learning, ensuring rewards and verifiers do not encourage shortcuts, and improving generalization without excessive computation or overthinking.

Latest papers

1,103 papers170 papers in the last four weeks, up 124% on the four weeks before. 1.0% of all new papers.

Mar 17, 2026

When and Why Does Unsupervised RL Succeed in Mathematical Reasoning? A Manifold Envelopment Perspective

Although outcome-based reinforcement learning (RL) significantly advances the mathematical reasoning capabilities of Large Language Models (LLMs), its reliance on computationally expensive ground-truth annotations imposes a severe scalability bottleneck. Unsupervised RL guided by intrinsic rewards offers a scalable alternative, yet it suffers from opaque training dynamics and catastrophic instability, such as policy collapse and reward hacking. In this paper, we first design and evaluate a suite of intrinsic rewards that explicitly enforce concise and certain generation. Second, to discover the boundaries of this approach, we test base models across a spectrum of intrinsic reasoning capabilities, revealing how a model's foundational logical prior dictates its success or failure. Finally, to demystify why certain configurations stabilize while others collapse, we introduce a novel geometric diagnostic lens, showing that successful cases are enveloped by manifolds. Ultimately, our work goes beyond merely demonstrating that enforcing concise and certain responses successfully boosts mathematical reasoning; we reveal when this unsupervised approach breaks down and geometrically diagnose why.

Zelin Zhang, Fei Cheng, Chenhui Chu

Kyoto University

Unsupervised RL Reinforcement Learning RL for Language Model Reasoning LLM Reasoning Intrinsic Reward Methods

Mar 17, 2026

Dual Consensus: Escaping from Spurious Majority in Unsupervised RLVR via Two-Stage Vote Mechanism

Current label-free RLVR approaches for large language models (LLMs), such as TTRL and Self-reward, have demonstrated effectiveness in improving the performance of LLMs on complex reasoning tasks. However, these methods rely heavily on accurate pseudo-label estimation and converge on spurious yet popular answers, thereby trapping in a dominant mode and limiting further improvements. Building on this, we propose Dual Consensus Reinforcement Learning (DCRL), a novel self-supervised training method which is capable of generating more reliable learning signals through a two-stage consensus mechanism. The model initially acts as an anchor, producing dominant responses; then it serves as an explorer, generating diverse auxiliary signals via a temporary unlearning process. The final training target is derived from the harmonic mean of these two signal sets. Notably, the process operates entirely without external models or supervision. Across eight benchmarks and diverse domains, DCRL consistently improves Pass@1 over majority vote while yielding more stable training dynamics. These results demonstrate that DCRL establishes a scalable path toward stronger reasoning without labels.

Kaixuan Du, Meng Cao, Hang Zhang +3

School of Automation Science and Electrical Engineering, Beihang University

RL for Language Model Reasoning Self-Training for Language Models Reinforcement Learning with Verifiable Rewards Self-Consistency in Language Models

Mar 17, 2026

DyJR: Preserving Diversity in Reinforcement Learning with Verifiable Rewards via Dynamic Jensen-Shannon Replay

While Reinforcement Learning (RL) enhances Large Language Model reasoning, on-policy algorithms like GRPO are sample-inefficient as they discard past rollouts. Existing experience replay methods address this by reusing accurate samples for direct policy updates, but this can incur additional storage costs and concentrate the policy on a narrow set of solutions. We argue that historical data should prioritize sustaining local policy plasticity rather than simply reinforcing accuracy. We define local policy plasticity as a persistent ability to remain backtrackable and switchable with respect to recent successful trajectories: throughout training, the policy maintains non-negligible support on recently reachable alternatives, so it can smoothly reallocate probability mass when needed without being locked into a single dominant path. To this end, we propose Dynamic Jensen-Shannon Replay (DyJR), a simple yet effective regularization framework using a dynamic reference distribution from recent trajectories. DyJR introduces two innovations: (1) A Time-Sensitive Dynamic Buffer that uses FIFO and adaptive sizing to retain only temporally proximal samples, synchronizing with model evolution; and (2) Jensen-Shannon Divergence Regularization, which replaces direct replay policy-gradient updates with a regularization signal that discourages premature over-commitment to a single Rank-1 trajectory. Experiments on mathematical reasoning, Text-to-SQL, and coding benchmarks demonstrate that DyJR improves over GRPO as well as baselines such as RLEP and Ex-GRPO, while maintaining training efficiency comparable to the original GRPO. Furthermore, Rank-k token probability evolution and semantic-mode analyses show reduced concentration and greater retention of alternative continuations. Matched admission-objective comparisons and repeated runs provide additional evidence for the roles of DyJR's components.

Long Li, Zhijian Zhou, Tianyi Wang +7

Griffith University, Australia · Fudan University, China · Shanghai Innovation Institute, China +3

Behavioral Diversity in RL Reinforcement Learning RL for Language Model Reasoning Experience Replay Reinforcement Learning with Verifiable Rewards

Mar 17, 2026

ARISE: Agent Reasoning with Intrinsic Skill Evolution in Hierarchical Reinforcement Learning

The dominant paradigm for improving mathematical reasoning in language models relies on Reinforcement Learning with verifiable rewards. Yet existing methods treat each problem instance in isolation without leveraging the reusable strategies that emerge and accumulate during training. To this end, we introduce ARISE (Agent Reasoning via Intrinsic Skill Evolution), a hierarchical reinforcement learning framework, in which a shared policy operates both to manage skills at high-level and to generate responses at low-level (denoted as a Skills Manager and a Worker, respectively). The Manager maintains a tiered skill library through a dedicated skill generation rollout that performs structured summarization of successful solution traces (after execution), while employing a policy-driven selection mechanism to retrieve relevant skills to condition future rollouts (before execution). A hierarchical reward design guides the co-evolution of reasoning ability and library quality. Experiments on two base models and seven benchmarks spanning both competition mathematics and Omni-MATH show that ARISE consistently outperforms GRPO-family algorithms and memory-augmented baselines, with particularly notable gains on out-of-distribution tasks. Ablation studies confirm that each component contributes to the observed improvements and that library quality and reasoning performance improve in tandem throughout training. Code is available at https://github.com/Skylanding/ARISE.

Yu Li, Rui Miao, Zhengling Qi +1

Department of Electrical and Computer Engineering, George Washington University · Department of Mathematical Sciences, University of Texas at Dallas · School of Business, George Washington University

RL for Language Model Reasoning LLM Mathematical Reasoning Agent Skill Learning Hierarchical RL

Mar 16, 2026

SAGE: Multi-Agent Self-Evolution for LLM Reasoning

Reinforcement learning with verifiable rewards improves reasoning in large language models (LLMs), but many methods still rely on large human-labeled datasets. While self-play reduces this dependency, it often lacks explicit planning and strong quality control, limiting stability in long-horizon multi-step reasoning. We present SAGE (Self-evolving Agents for Generalized reasoning Evolution), a closed-loop framework where four agents: Challenger, Planner, Solver, and Critic, co-evolve from a shared LLM backbone using only a small seed set. The Challenger continuously generates increasingly difficult tasks; the Planner converts each task into a structured multi-step plan; and the Solver follows the plan to produce an answer, whose correctness is determined by external verifiers. The Critic scores and filters both generated questions and plans to prevent curriculum drift and maintain training signal quality, enabling stable self-training. Across mathematics and code-generation benchmarks, SAGE delivers consistent gains across model scales, improving the Qwen-2.5-7B model by 8.9% on LiveCodeBench and 10.7% on OlympiadBench.

Yulin Peng, Xinxin Zhu, Chenxing Wei +4

College of Computer Science and Software Engineering, Shenzhen University, China · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), China · School of Information Technology, Carleton University, Canada

LLM Reasoning Self-Training for Language Models RL for Language Model Reasoning Multi-Agent LLMs Code Generation

Mar 15, 2026

PA3: Policy-Aware Agent Alignment through Chain-of-Thought

Conversational assistants powered by large language models (LLMs) excel at tool-use tasks but struggle with adhering to complex, business-specific rules. While models can reason over business rules provided in context, including all policies for every query introduces high latency and wastes compute. Furthermore, these lengthy prompts lead to long contexts, harming overall performance due to the 'needle-in-a-haystack' problem. To address these challenges, we propose a multi-stage alignment method that teaches models to recall and apply relevant business policies during chain-of-thought reasoning at inference time, without including the full business policy in-context. Furthermore, we introduce a novel Policy Recall reward based on the Jaccard score and a Hallucination Penalty for GRPO training. Altogether, our best model outperforms the baseline by 16 points and surpasses comparable in-context baselines of similar model size by 3 points, while using 40% fewer words.

Shubhashis Roy Dipta, Daniel Bis, Kun Zhou +4

University of Maryland, Baltimore County · Amazon Alexa AI

LLM Alignment RL for Language Model Reasoning

Mar 15, 2026

An Industrial-Scale Insurance LLM Achieving Verifiable Domain Mastery and Hallucination Control without Competence Trade-offs

Adapting Large Language Models (LLMs) to high-stakes vertical domains like insurance presents a significant challenge: scenarios demand strict adherence to complex regulations and business logic with zero tolerance for hallucinations. Existing approaches often suffer from a Competency Trade-off - sacrificing general intelligence for domain expertise - or rely heavily on RAG without intrinsic reasoning. To bridge this gap, we present INS-S1, an insurance-specific LLM family trained via a novel end-to-end alignment paradigm. Our approach features two methodological innovations: (1) A Verifiable Data Synthesis System that constructs hierarchical datasets for actuarial reasoning and compliance; and (2) A Progressive SFT-RL Curriculum Framework that integrates dynamic data annealing with a synergistic mix of Verified Reasoning (RLVR) and AI Feedback (RLAIF). By optimizing data ratios and reward signals, this framework enforces domain constraints while preventing catastrophic forgetting. Additionally, we release INSEva, the most comprehensive insurance benchmark to date (39k+ samples). Extensive experiments show that INS-S1 achieves SOTA performance on domain tasks, significantly outperforming DeepSeek-R1 and Gemini-2.5-Pro. Crucially, it maintains top-tier general capabilities and achieves a record-low 0.6% hallucination rate (HHEM). Our results demonstrate that rigorous domain specialization can be achieved without compromising general intelligence.

Qian Zhu, Xinnan Guo, Jingjing Huo +5

Ant Group

Domain Adaptation for LLMs LLM Alignment LLM Hallucination Mitigation RL for Language Model Reasoning LLM Evaluation

Mar 15, 2026

From $\log π$ to $π$ : Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed a leap in Large Language Model (LLM) reasoning, yet its optimization dynamics remain fragile. Standard algorithms like GRPO enforce stability via "hard clipping", which inadvertently stifles exploration by discarding gradients of tokens outside the trust region. While recent "soft clipping" methods attempt to recover these gradients, they suffer from a critical challenge: relying on log-probability gradient (

\nabla_θ\log π_θ

) yields divergent weights as probabilities vanish, destabilizing LLM training. We rethink this convention by establishing probability gradient (

\nabla_θπ_θ

) as the superior optimization primitive. Accordingly, we propose Decoupled Gradient Policy Optimization (DGPO), which employs a decoupled decay mechanism based on importance sampling ratios. By applying asymmetric, continuous decay to boundary tokens, DGPO resolves the conflict between stability and sustained exploration. Extensive experiments across DeepSeek-R1-Distill-Qwen series models (1.5B/7B/14B) demonstrate that DGPO consistently outperforms strong baselines on various mathematical benchmarks, offering a robust and scalable solution for RLVR. Our code and implementation are available at: https://github.com/FlyTune/DGPO-RL.

Xiaoliang Fu, Jiaye Lin, Yangyi Fang +6

Meituan · Fudan University · Tsinghua University +2

RL for Language Model Reasoning Policy Gradient Methods RL Post-Training Policy Gradient Reinforcement Learning with Verifiable Rewards

Mar 14, 2026

GRPO and Reflection Reward for Mathematical Reasoning in Large Language Models

The enhancement of reasoning capabilities in large language models (LLMs) has garnered significant attention, with supervised fine-tuning (SFT) and reinforcement learning emerging as dominant paradigms. While recent studies recognize the importance of reflection in reasoning processes, existing methodologies seldom address proactive reflection encouragement during training. This study focuses on mathematical reasoning by proposing a four-stage framework integrating Group Relative Policy Optimization (GRPO) with reflection reward mechanisms to strengthen LLMs' self-reflective capabilities. Besides, this approach incorporates established accuracy and format reward. Experimental results demonstrate GRPO's state-of-the-art performance through reflection-encouraged training, with ablation studies confirming the reflection reward's pivotal role. Comparative evaluations demonstrate full-parameter SFT's superiority over low-rank adaptation (LoRA) despite heightened computational demands. Building on these cumulative findings, this research substantiates GRPO's methodological significance in post-training optimization and envisions its potential to serve as a pivotal enabler for future LLM-based intelligent agents through the synergistic integration of cognitive rewards with dynamic environmental interactions.

Zhijie Wang

School of Computer Science and Engineering, Sun Yat-sen University(SYSU), Guangzhou, China

Self-Reflection in Language Model Agents LLM Reasoning RL for Language Model Reasoning RL Post-Training Metacognition in Language Models Group Relative Policy Optimization

Mar 14, 2026

MHPO: Modulated Hazard-aware Policy Optimization for Stable Reinforcement Learning

Regulating the importance ratio is critical for the training stability of Group Relative Policy Optimization (GRPO) based frameworks. However, prevailing ratio control methods, such as hard clipping, suffer from non-differentiable boundaries and vanishing gradient regions, failing to maintain gradient fidelity. Furthermore, these methods lack a hazard-aware mechanism to adaptively suppress extreme deviations, leaving the optimization process vulnerable to abrupt policy shifts. To address these challenges, we propose Modulated Hazard-aware Policy Optimization (MHPO), a novel framework designed for robust and stable reinforcement learning. The proposed MHPO introduces a Log-Fidelity Modulator (LFM) to map unbounded importance ratios into a bounded, differentiable domain. This mechanism effectively prevents high-variance outlier tokens from destabilizing the loss landscape while ensuring global gradient stability. Complementarily, a Decoupled Hazard Penalty (DHP) integrates cumulative hazard functions from survival analysis to independently regulate positive and negative policy shifts. By shaping the optimization landscape with hazard-aware penalties, the proposed MHPO achieves fine-grained regulation of asymmetric policy shifts simultaneously mitigating mode collapse from over-expansion and preventing policy erosion from catastrophic contraction within a stabilized trust region. Extensive evaluations on diverse reasoning benchmarks across both text-based and vision-language tasks demonstrate that MHPO consistently outperforms existing methods, achieving superior performance while significantly enhancing training stability.

Hongjun Wang, Wei Liu, Weibo Gu +2

The University of Hong Kong · Tencent Youtu Lab

Policy Gradient Methods RL for Language Model Reasoning Group Relative Policy Optimization

Mar 13, 2026

MemReward: Graph-Based Experience Memory for LLM Reward Prediction with Limited Labels

Reinforcement learning has emerged as a powerful paradigm for improving large language model (LLM) reasoning, where rollouts are sampled from the policy and reward signals computed on those rollouts are used to update the policy. However, in data-scarce scenarios, obtaining ground-truth labels to verify rollouts at scale often requires expensive human annotation or labor-intensive expert verification. For instance, evaluating mathematical proofs demands expert review, and open-ended question answering lacks definitive ground truth. When ground-truth labels are scarce, the effectiveness of reinforcement learning fine-tuning is constrained. Inspired by the success of semi-supervised learning in propagating labels from labeled to unlabeled samples, we propose MemReward, a graph-based experience memory framework that integrates reward propagation directly into online policy optimization. MemReward stores rollouts (thinking processes and final answers) from an initial LLM policy as nodes in a heterogeneous graph connected by similarity and structural edges, over which a GNN propagates rewards from labeled to unlabeled rollouts. To train such a framework, we first warm up the GNN on labeled rollouts to predict rewards via heterogeneous aggregation over query, thinking, and answer nodes. During online RL fine-tuning, unlabeled rollouts are attached to the graph by query similarity, and the GNN predicts their rewards, yielding a hybrid reward acquisition strategy that combines ground-truth and GNN-predicted rewards. Experiments on Qwen2.5-1.5B and 3B in mathematics, question answering, and code generation demonstrate that MemReward, with ground-truth rewards on only 20% of rollouts, achieves 96.6% of Oracle performance on 1.5B and 97.3% on 3B, and closely approaches Oracle on out-of-domain tasks.

Tianyang Luo, Tao Feng, Zhigang Hua +4

University of Illinois Urbana-Champaign · Meta

RL for Language Model Reasoning RL Fine-Tuning Reward Modeling

Mar 13, 2026

When Right Meets Wrong: Bilateral Context Conditioning with Reward-Confidence Correction for GRPO

Group Relative Policy Optimization (GRPO) has emerged as an effective method for training reasoning models. While it computes advantages based on group mean, GRPO treats each output as an independent sample during the optimization and overlooks a vital structural signal: the natural contrast between correct and incorrect solutions within the same group, thus ignoring the rich, comparative data that could be leveraged by explicitly pitting successful reasoning traces against failed ones. To capitalize on this, we present a contrastive reformulation of GRPO, showing that the GRPO objective implicitly maximizes the margin between the policy ratios of correct and incorrect samples. Building on this insight, we propose Bilateral Context Conditioning (BICC), a mechanism that allows the model to cross-reference successful and failed reasoning traces during the optimization, enabling a direct information flow across samples. We further introduce Reward-Confidence Correction (RCC) to stabilize training by dynamically adjusts the advantage baseline in GRPO using reward-confidence covariance derived from the first-order approximation of the variance-minimizing estimator. Both mechanisms require no additional sampling or auxiliary models and can be adapted to all GRPO variants. Experiments on mathematical reasoning benchmarks demonstrate consistent improvements across comprehensive models and algorithms. Code is available at https://github.com/Skylanding/BiCC.

Yu Li, Tian Lan, Zhengling Qi

Department of Electrical and Computer Engineering, George Washington University · School of Business, George Washington University

RL for Language Model Reasoning Group Relative Policy Optimization LLM Reasoning Contrastive RL

Mar 13, 2026

Beyond Final Answers: CRYSTAL Benchmark for Transparent Multimodal Reasoning Evaluation

We introduce CRYSTAL (Clear Reasoning via Yielded Steps, Traceability, and Logic), a diagnostic benchmark with 6,372 instances that evaluates multimodal reasoning through verifiable intermediate steps. We propose two complementary metrics: Match F1, which scores step-level precision and recall via semantic similarity matching, and Ordered Match F1, which further penalizes disordered reasoning chains. References are constructed through a Delphi-inspired pipeline in which four independent MLLMs generate trajectories, which are then aggregated via semantic clustering and validated through human quality gates. Evaluation of 20 MLLMs, including commercial frontier systems not used during benchmark construction, reveals systematic failures that are invisible to answer accuracy: universal cherry-picking (precision far exceeds recall), non-monotonic scaling trade-offs, and disordered reasoning in which no competitive model preserves more than 60% of matched steps in the correct order. Beyond evaluation, we propose the Causal Process Reward (CPR), a multiplicative reward that couples answer correctness with step-level alignment, and CPR-Curriculum, which progressively increases reasoning difficulty during training. CPR-Curriculum achieves a 32% improvement in Match F1 via GRPO where additive reward strategies fail, improving reasoning without manual step annotation.

Wayner Barrios, SouYoung Jin

Dartmouth College, Hanover, NH, USA

Reasoning Evaluation MLLM Reasoning Multimodal Model Evaluation Multimodal CoT Reasoning Process Reward Models RL for Language Model Reasoning

Mar 13, 2026

Test-time RL alignment exposes task familiarity artifacts in LLM benchmarks

Direct evaluation of LLMs on benchmarks can be misleading because comparatively strong performance may reflect task familiarity rather than capability. The train-before-test approach controls for task familiarity by giving each model task-relevant training before evaluation, originally through supervised finetuning. However, suitable training data is often hard to come by, and evaluation results vary with the data chosen. In this paper, we propose a two-stage test-time reinforcement learning (RL) alignment method for train-before-test. First, RL with a single sample provides a first alignment of the model to the task format, and second, test-time RL with majority-voting reward aligns the model to the benchmark distribution. Our test-time RL alignment method aligns similarly well as SFT-based train-before test, but without requiring a task-specific training set. On a domain-specific benchmark without training data, we show that direct evaluation underestimates base models which perform substantially better once aligned, yielding a more faithful evaluation of their capabilities. Moreover, for reasoning tasks, the performance gap between fine-tuned models and their base models largely disappears after alignment, suggesting that many gains from RLVR/SFT reported in the literature are not a difference in reasoning capability, but rather artifacts of task familiarity.

Kun Wang, Reinhard Heckel

School of Computation, Information and Technology, Technical University of Munich · Munich Center for Machine Learning

LLM Evaluation Inference-Time Language Model Alignment Test-Time RL RL for Language Model Reasoning

Mar 13, 2026

Rethinking Multiple-Choice Questions for RLVR: Unlocking Potential via Distractor Design

Reinforcement Learning with Verifiable Rewards (RLVR) significantly enhances the reasoning capabilities of Large Language Models. When applied to RLVR, Multiple-Choice Questions (MCQs) offer a scalable source of verifiable data but risk inducing reward hacking, where models shortcut reasoning via random guessing or simple elimination. Current approaches often mitigate this by converting MCQs to open-ended formats, thereby discarding the contrastive signal provided by expert-designed distractors. In this work, we systematically investigate the impact of option design on RLVR. Our analysis highlights two primary insights: (1) Mismatches in option counts between training and testing degrade performance. (2) Strong distractors effectively mitigate random guessing, enabling effective RLVR training even with 2-way questions. Motivated by these findings, we propose Iterative Distractor Curation (IDC), a framework that actively constructs high-quality distractors to block elimination shortcuts and promote deep reasoning. Experiments on various benchmarks demonstrate that our method effectively enhances distractor quality and yields significant gains in RLVR training compared to the original data.

Xu Guo, Qiming Ge, Jian Tong +8

Shanghai AI Laboratory · Shanghai Innovation Institute · Fudan University

RL for Language Model Reasoning Multiple-Choice Question Answering Reward Hacking Reinforcement Learning with Verifiable Rewards

Mar 13, 2026

Reinforcement Learning for Diffusion LLMs with Entropy-Guided Step Selection and Stepwise Advantages

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive an exact, unbiased policy gradient that decomposes over denoising steps and is expressed in terms of intermediate advantages, without requiring explicit evaluation of the sequence likelihood. To obtain a practical and compute-efficient estimator, we (i) select denoising steps for policy updates via an entropy-guided approximation bound, and (ii) estimate intermediate advantages using a one-step denoising reward naturally provided by the diffusion model, avoiding costly multi-step rollouts. Experiments on coding and logical reasoning benchmarks demonstrate state-of-the-art results, with strong competitive performance on mathematical reasoning, outperforming existing RL post-training approaches for DLMs. Code is available at https://github.com/vishnutez/egspo-dllm-rl.

Vishnu Teja Kunde, Fatemeh Doudi, Mahdi Farahbakhsh +3

Department of Electrical & Computer Engineering, Texas A&M University, College Station, TX 77843

RL for Diffusion Models Diffusion Language Model Training RL for Language Model Reasoning Diffusion Language Models

Mar 12, 2026

LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.

Haiying Xu, Zihan Wang, Song Dai +3

The Hong Kong University of Science and Technology (Guangzhou) · Nankai University · Communication University of China

Multimodal Large Language Models Multimodal Reasoning Latent Visual Reasoning Geometric Representation Learning Mathematical Reasoning Benchmarks RL for Language Model Reasoning

Mar 12, 2026

Entropy-Preserving Reinforcement Learning

Policy gradient algorithms have driven many recent advancements in language model reasoning. An appealing property is their ability to learn from exploration on their own trajectories, a process crucial for fostering diverse and creative solutions. As we show in this paper, many policy gradient algorithms naturally reduce the entropy -- and thus the diversity of explored trajectories -- as part of training, yielding a policy increasingly limited in its ability to explore. In this paper, we argue that entropy should be actively monitored and controlled throughout training. We formally analyze the contributions of leading policy gradient objectives on entropy dynamics, identify empirical factors (such as numerical precision) that significantly impact entropy behavior, and propose explicit mechanisms for entropy control. These include REPO, a family of algorithms that modify the advantage function to regulate entropy, and ADAPO, an adaptive asymmetric clipping approach. Models trained with our entropy-preserving methods maintain diversity throughout training, yielding final policies that are more performant and retain their trainability for sequential learning in new environments.

Aleksei Petrenko, Ben Lipkin, Kevin Chen +4

Apple · MIT

Policy Gradient Methods Behavioral Diversity in RL RL for Language Model Reasoning Maximum Entropy RL

Mar 11, 2026

Hindsight-Anchored Policy Optimization: Learning Through Hindsight with Thompson Sampling-Inspired Adaptive Gating

Reinforcement Learning with Verifiable Rewards improves reasoning in large language models, yet on-policy learning often suffers from cold-start challenges in sparse-reward settings. Recent mixed-policy approaches address this by combining off-policy teacher data with on-policy training. However, simply combining these introduce a persistent off-policy gradient mass that risks training collapse and instability. To address this challenge, we propose Hindsight-Anchored Policy Optimization (HAPO), a framework that allows teacher intervention to act as a temporary support. HAPO employs Beta-Binomial confidence gating, an adaptive gating mechanism that decides when to open the gate for teacher intervention. The intervention operates with Synthetic Success Injection, which replaces the group's lowest-reward rollout with a verified teacher trajectory. We also introduce adaptive threshold annealing, which gradually retracts the support and restores on-policy training within a finite horizon to mitigate persistent off-policy drift. We demonstrate that HAPO can be layered on top of existing mixed-policy methods in a generalizable manner. Across six math reasoning benchmarks and two model scales, HAPO improves the average accuracy of three major mixed-policy methods while maintaining training stability.

Yuning Wu, Ke Wang, Haoran Liu +3

Amazon

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Sparse-Reward RL Off-Policy RL

Mar 11, 2026

DeReason: A Difficulty-Aware Curriculum Improves Decoupled SFT-then-RL Training for General Reasoning

Reinforcement learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for eliciting reasoning capabilities in large language models, particularly in mathematics and coding. While recent efforts have extended this paradigm to broader general scientific (STEM) domains, the complex interplay between supervised fine-tuning (SFT) and RL in these contexts remains underexplored. In this paper, we conduct controlled experiments revealing a critical challenge: for general STEM domains, RL applied directly to base models is highly sample-inefficient and is consistently surpassed by supervised fine-tuning (SFT) on moderate-quality responses. Yet sequential SFT followed by RL can further improve performance, suggesting that the two stages play complementary roles, and that how training data is allocated between them matters. Therefore, we propose DeReason, a difficulty-based data decoupling strategy for general reasoning. DeReason partitions training data by reasoning intensity estimated via LLM-based scoring into reasoning-intensive and non-reasoning-intensive subsets. It allocates broad-coverage, non-reasoning-intensive problems to SFT to establish foundational domain knowledge, and reserves a focused subset of difficult problems for RL to cultivate complex reasoning. We demonstrate that this principled decoupling yields better performance than randomly splitting the data for sequential SFT and RL. Extensive experiments on general STEM and mathematical benchmarks demonstrate that our decoupled curriculum training significantly outperforms SFT-only, RL-only, and random-split baselines. Our work provides a systematic study of the interplay between SFT and RL for general reasoning, offering a highly effective and generalized post-training recipe.

Hanxu Hu, Yuxuan Wang, Maggie Huan +4

University of Zurich · University of Pennsylvania · ETH Zurich +2

RL for Language Model Reasoning RL Fine-Tuning Scientific Reasoning in Language Models Curriculum RL Curriculum Learning Numerical Reasoning in Language Models

Mar 11, 2026

TIPS: Turn-Level Information-Potential Reward Shaping for Search-Augmented LLMs

Search-augmented large language models (LLMs) trained with reinforcement learning (RL) have achieved strong results on open-domain question answering (QA), but training still remains a significant challenge. The optimization is often unstable due to sparse rewards and difficult credit assignments across reasoning and tool calls. To address this, we introduce Turn-Level Information Potential Reward Shaping (TIPS), a simple framework that assigns dense, turn-level rewards to each reasoning + tool-call segment based on the increased likelihood of the correct answer under a teacher model. By leveraging the potential-based reward shaping, TIPS offers fine-grained and policy-invariant guidance that overcomes the limitations of outcome-only optimization. Evaluated on seven QA benchmarks, TIPS consistently outperforms GRPO/PPO baselines and substantially improves training stability. For instance, with a Qwen-2.5 7B Instruct model, TIPS improves the average Exact Match score by 11.8% and F1 by 13.6% relative to PPO. Our results demonstrate that turn-level information-potential reward shaping provides an effective and general solution to sparse-reward credit assignment for multi-turn LLM reasoning.

Yutao Xie, Nathaniel Thomas, Nicklas Hansen +3

UC San Diego · AWS AI

RL for Language Model Reasoning Reward Shaping RL for Tool Use Sparse-Reward RL Open-Domain QA

Mar 11, 2026

Scaling Reasoning Efficiently via Relaxed On-Policy Distillation

On-policy distillation (OPD) is a promising approach for transferring reasoning capabilities to capacity-constrained models, yet sampled-token OPD often suffers from entropy collapse and negative transfer. We identify uniform credit allocation as a key bottleneck: existing objectives obtain dense teacher feedback on student-generated trajectories, but apply it uniformly across sampled tokens despite highly heterogeneous token-level signals. Most tokens carry redundant near-zero credit, while rare heavy-tailed negative credits can dominate updates and prematurely suppress plausible reasoning trajectories. We introduce REOPOLD (Relaxed On-Policy Distillation), a framework that relaxes this uniform assignment by controlling where teacher feedback is applied, how strongly it affects the update, and when the allocation rule changes during training. Across diverse reasoning tasks, REOPOLD improves sampled-token OPD over recent post-training baselines with up to 12x higher sample efficiency, and extends to cross-vocabulary distillation, self-distillation, and test-time scaling.

Jongwoo Ko, Sara Abdali, Young Jin Kim +2

On-Policy Distillation RL for Language Model Reasoning Sample-Efficient RL

Mar 11, 2026

Dynamics-Predictive Sampling for Active RL Finetuning of Large Reasoning Models

Reinforcement learning (RL) finetuning has become a key technique for enhancing the reasoning abilities of large language models (LLMs). However, its effectiveness critically depends on the selection of training data. Recent advances underscore the importance of online prompt selection methods, which typically concentrate training on partially solved or moderately challenging examples under the current policy, thereby yielding more effective model updates. While significantly accelerating RL finetuning in terms of training steps, they also incur substantial computational overhead by requiring extensive LLM rollouts over large candidate batches to identify informative samples, an expense that can outweigh the finetuning process itself. To address this challenge, this work proposes Dynamics-Predictive Sampling (DPS), which online predicts and selects informative prompts by inferring their learning dynamics prior to costly rollouts. Specifically, we introduce a new perspective by modeling each prompt's solving progress during RL finetuning as a dynamical system, where the extent of solving is represented as the state and the transition is characterized by a hidden Markov model. Using historical rollout reward signals, we perform online Bayesian inference to estimate evolving state distributions, and the inference outcome provides a predictive prior for efficient prompt selection without rollout-intensive filtering. Empirical results across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that DPS substantially reduces redundant rollouts, accelerates the training process, and achieves superior reasoning performance.

Yixiu Mao, Yun Qu, Qi Wang +2

Department of Automation, Tsinghua University

Prompt Selection for RL RL for Language Model Reasoning RL Fine-Tuning Large Reasoning Models

Mar 11, 2026

mAceReason-Math: A Dataset of High-Quality Multilingual Math Problems Ready For RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has been successfully applied to significantly boost the capabilities of pretrained large language models, especially in the math and logic problem domains. However, current research and available training datasets remain English-centric. While multilingual training data and benchmarks have been created in the past, they were not created with RLVR and current model capability in mind, and their level of difficulty is often too low to provide appropriate training signals for current models. To address this gap, we provide mAceReason-Math, a dataset of high-quality translations of challenging math problems sourced from a corpus specifically curated for RLVR (AceReason-Math). We further take specific care to clean and improve our translations, resulting in a coverage of 14 languages with more than 10,000 samples per language. We release the dataset to facilitate multilingual RLVR research and benchmarking in the research community.

Konstantin Dobler, Simon Lehnerer, Federico Scozzafava +2

Apple · Hasso Plattner Institute & ELLIS Unit Potsdam

LLM Mathematical Reasoning Mathematical Reasoning RL for Language Model Reasoning

Mar 11, 2026

Reinforcement Learning with Conditional Expectation Reward

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective in enhancing the reasoning capabilities of large language models, particularly in domains such as mathematics where reliable rule-based verifiers can be constructed. However, the reliance on handcrafted, domain-specific verification rules substantially limits the applicability of RLVR to general reasoning domains with free-form answers, where valid answers often exhibit significant variability, making it difficult to establish complete and accurate rules. To address this limitation, we propose Conditional Expectation Reward (CER), which leverages the large language model itself as an implicit verifier, and is therefore applicable to general domains and eliminates the need for external verifiers or auxiliary models. CER is defined as the expected likelihood of generating the reference answer conditioned on the generated answer. In contrast to rule-based verifiers that yield binary feedback, CER provides a soft, graded reward signal that reflects varying degrees of correctness, making it better suited to tasks where answers vary in correctness. Experimental results demonstrate that CER is effective across a wide range of reasoning tasks, spanning both mathematical and general domains, indicating that CER serves as a flexible and general verification mechanism. The code is available at https://github.com/changyi7231/CER.

Changyi Xiao, Caijun Xu, Yixin Cao

Fudan University

RL for Language Model Reasoning LLM Answer Verification Reinforcement Learning with Verifiable Rewards

Mar 10, 2026

CLIPO: Contrastive Learning in Policy Optimization Generalizes RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capacity of Large Language Models (LLMs). However, RLVR solely relies on final answers as outcome rewards, neglecting the correctness of intermediate reasoning steps. Training on these process-wrong but outcome-correct rollouts can lead to hallucination and answer-copying, severely undermining the model's generalization and robustness. To address this, we incorporate a Contrastive Learning mechanism into the Policy Optimization (CLIPO) to generalize the RLVR process. By optimizing a contrastive loss over successful rollouts, CLIPO steers the LLM to capture the invariant structure shared across correct reasoning paths. This provides a more robust cross-trajectory regularization than the original single-path supervision in RLVR, effectively mitigating step-level reasoning inconsistencies and suppressing hallucinatory artifacts. In experiments, CLIPO consistently improves multiple RLVR baselines across diverse reasoning benchmarks, demonstrating uniform improvements in generalization and robustness for policy optimization of LLMs. Our code and training recipes are available at https://github.com/Qwen-Applications/CLIPO.

Sijia Cui, Pengyu Cheng, Jiajun Song +6

Qwen Large Model Application Team, Alibaba · Institute of Automation, Chinese Academy of Sciences

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Reasoning Consistency in Language Models Contrastive RL

Mar 10, 2026

Good Reasoning Makes Good Demonstrations: Implicit Reasoning Quality Supervision via In-Context Reinforcement Learning

Reinforcement Learning with Verifiable Rewards (RLVR) improves reasoning in large language models but treats all correct solutions equally, potentially reinforcing flawed traces that arrive at correct answers by chance. We observe that better reasoning makes better demonstrations: high-quality solutions serve as more effective in-context examples than low-quality ones. We term this teaching ability Demonstration Utility, and show that the policy model's own in-context learning ability provides an efficient way to measure it, yielding a quality signal termed Evidence Gain. To leverage this signal during training, we introduce In-Context RLVR, which prepends demonstrations before each rollout. Theoretically, we prove that this simple input modification implicitly reweights rewards by a factor approximately proportional to Evidence Gain, assigning higher weights to high-quality traces without requiring costly computation. Experiments on mathematical reasoning benchmarks demonstrate consistent improvements in both accuracy and reasoning quality over standard RLVR baselines. Our codes and datasets are available at https://github.com/Mithas-114/IC-DAPO.

Tiehua Mei, Minxuan Lv, Leiyu Pan +5

School of Data Science, Fudan University · University of Chinese Academy of Sciences · College of Intelligence and Computing, Tianjin University

RL for Language Model Reasoning LLM Reasoning In-Context RL Reinforcement Learning with Verifiable Rewards Reasoning Evaluation

Mar 10, 2026

C2F-Thinker: Coarse-to-Fine Reasoning with Hint-Guided Reinforcement Learning for Multimodal Sentiment Analysis

Multimodal sentiment analysis aims to integrate textual, acoustic, and visual information for deep emotional understanding. Despite the progress of multimodal large language models (MLLMs) via supervised fine-tuning, their "black-box" nature hinders interpretability. While Chain-of-Thought (CoT) reasoning offers a potential remedy, it is constrained by high manual annotation costs and the inherent challenges of reinforcement learning (RL), such as reward sparsity and low exploration efficiency on hard samples. This paper presents C2F-Thinker, a framework that harmonizes coarse-to-fine structured reasoning with hint-guided RL through a two-stage progressive training pipeline. In the first stage, we conduct cold-start supervised fine-tuning using high-quality CoT data distilled from a larger teacher model, consisting of three distinct phases: polarity judgment, intermediate analysis, and fine-grained scoring. This equips the base model with a structured emotional reasoning paradigm. In the second stage, we introduce a hint-guided Group Relative Policy Optimization (GRPO) algorithm. By injecting correct initial polarity predictions as hints during the sampling process, the model is guided toward accurate reasoning paths, effectively mitigating cascading errors and enhancing the utilization of hard samples. Furthermore, a multi-faceted reward function incorporating classification, regression, and formatting constraints is designed to refine prediction accuracy while preserving interpretability. Experimental results demonstrate that C2F-Thinker achieves competitive performance on fine-grained sentiment regression tasks while significantly outperforming baselines in cross-domain generalization. This highlights its potential in building trustworthy and robust sentiment analysis systems for real-world applications.

Miaosen Luo, Zhenhao Yang, Jieshen Long +3

School of Computer Science, South China Normal University Guangzhou, Guangdong, China · School of Electronic and Information Engineering, South China University of Technology Guangzhou, Guangdong, China

Sentiment Analysis Multimodal Sentiment Analysis Multimodal CoT Reasoning RL for Language Model Reasoning

Mar 10, 2026

Social-R1: Towards Human-like Social Reasoning in LLMs

While large language models demonstrate remarkable capabilities across numerous domains, social intelligence - the capacity to perceive social cues, infer mental states, and generate appropriate responses - remains a critical challenge, particularly for enabling effective human-AI collaboration and developing AI that truly serves human needs. Current models often rely on superficial patterns rather than genuine social reasoning. We argue that cultivating human-like social intelligence requires training with challenging cases that resist shortcut solutions. To this end, we introduce ToMBench-Hard, an adversarial benchmark designed to provide hard training examples for social reasoning. Building on this, we propose Social-R1, a reinforcement learning framework that aligns model reasoning with human cognition through multi-dimensional rewards. Unlike outcome-based RL, Social-R1 supervises the entire reasoning process, enforcing structural alignment, logical integrity, and information density. Results show that our approach enables a 4B parameter model to surpass much larger counterparts and generalize robustly across eight diverse benchmarks. These findings demonstrate that challenging training cases with trajectory-level alignment offer a path toward efficient and reliable social intelligence.

Jincenzi Wu, Yuxuan Lei, Jianxun Lian +5

The Chinese University of Hong Kong · Microsoft Research Asia · Princeton University

Social Reasoning RL for Language Model Reasoning Theory of Mind Process Supervision

Mar 10, 2026

Decoupling Reasoning and Confidence: Resurrecting Calibration in Reinforcement Learning from Verifiable Rewards

Reinforcement Learning from Verifiable Rewards (RLVR) significantly enhances large language models (LLMs) reasoning but severely suffers from calibration degeneration, where models become excessively over-confident in incorrect answers. Previous studies devote to directly incorporating calibration objective into existing optimization target. However, our theoretical analysis demonstrates that there exists a fundamental gradient conflict between the optimization for maximizing policy accuracy and minimizing calibration error. Building on this insight, we propose DCPO, a simple yet effective framework that systematically decouples reasoning and calibration objectives. Extensive experiments demonstrate that our DCPO not only preserves accuracy on par with GRPO but also achieves the best calibration performance and substantially mitigates the over-confidence issue. Our study provides valuable insights and practical solution for more reliable LLM deployment.

Zhengzhao Ma, Xueru Wen, Boxi Cao +6

Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China +2

Reinforcement Learning RL for Language Model Reasoning Language Model Calibration Reinforcement Learning with Verifiable Rewards