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 23, 2026

On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference

Δ\log p

between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that

Δ\log p

more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned

Δ\log p

direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher

Δ\log p

) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Kexin Huang, Haoming Meng, Junkang Wu +10

Alibaba Group

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

Mar 23, 2026

P^2O: Joint Policy and Prompt Optimization

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but is suffer from advantage collapse: when all rollouts of a query receive identical rewards, the group variance vanishes, most damagingly on hard samples, where scaling rollout budgets yields little. We introduce Joint Policy and Prompt Optimization (P O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P O mines hard samples with a success-rate threshold, evolves reasoning prompts for them with GEPA, and internalizes the elicited trajectories via context distillation, which optimizes each trajectory under the original query and thus removes inference-time prompting, with a Context Ratio Mask (CRM) filtering out extreme likelihood ratios. P O restores critical advantage signals and surpasses the GRPO baseline by up to 8.2 points in average accuracy on six held-out benchmarks across all training datasets and backbones, while also outperforming DAPO and other baselines. The gains are especially pronounced on hard benchmarks, reaching up to 16.3 points above GRPO on average across AIME24 and AIME25. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates provides a self-reinforcing framework that facilitates more effective LLM alignment.

Xinyu Lu, Kaiqi Zhang, Jinglin Yang +6

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

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Prompt Optimization Sparse-Reward RL

Mar 23, 2026

Adaptive Robust Estimator for Multi-Agent Reinforcement Learning

Multi-agent collaboration has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models, yet it suffers from interaction-level ambiguity that blurs generation, critique, and revision, making credit assignment across agents difficult. Moreover, policy optimization in this setting is vulnerable to heavy-tailed and noisy rewards, which can bias advantage estimation and trigger unstable or even divergent training. To address both issues, we propose a robust multi-agent reinforcement learning framework for collaborative reasoning, consisting of two components: Dual-Agent Answer-Critique-Rewrite (DACR) and an Adaptive Robust Estimator (ARE). DACR decomposes reasoning into a structured three-stage pipeline: answer, critique, and rewrite, while enabling explicit attribution of each agent's marginal contribution to its partner's performance. ARE provides robust estimation of batch experience means during multi-agent policy optimization. Across mathematical reasoning and embodied intelligence benchmarks, even under noisy rewards, our method consistently outperforms the baseline in both homogeneous and heterogeneous settings. These results indicate stronger robustness to reward noise and more stable training dynamics, effectively preventing optimization failures caused by noisy reward signals.

Zhongyi Li, Wan Tian, Jingyu Chen +8

Beihang University · Peking University · Chinese Academy of Sciences +1

Multi-Agent Reinforcement Learning RL for Language Model Reasoning Multi-Agent Collaboration Multi-Agent Reasoning Robust RL

Mar 23, 2026

Counterfactual Credit Policy Optimization for Multi-Agent Collaboration

Collaborative multi-agent large language models (LLMs) can solve complex reasoning tasks by decomposing roles, but reinforcement learning for such systems is limited by credit assignment: shared terminal rewards obscure individual contributions and can encourage free-riding. We introduce two optimizer-agnostic credit assignment methods for converting joint outcomes into agent-specific learning signals. Counterfactual Credit for Policy Optimization (CCPO) estimates an agent's marginal contribution by comparing the realized joint outcome with a counterfactual outcome where that agent is removed. Self-Evaluated Credit for Policy Optimization (SEPO) uses constrained self- and peer-evaluations as a verifier-anchored credit signal while keeping the external task outcome dominant. Both operate at the reward-construction layer rather than as policy optimizers, producing role-specific rewards or advantages for GRPO, GSPO, or REINFORCE++. We instantiate these credit signals in a sequential Think--Solve setting and evaluate them on mathematical reasoning benchmarks. Results show that explicit credit assignment often improves dual-agent reasoning, especially on MATH500 and several out-of-distribution settings, while gains vary across models and datasets. Our code is available at: https://github.com/bhai114/ccpo.

Zhongyi Li, Wan Tian, Jinju Chen +4

Beihang University · Peking University · Beijing University of Posts and Telecommunications

Counterfactual Credit Assignment RL for Language Model Reasoning Multi-Agent Collaboration

Mar 22, 2026

KG-Hopper: Empowering Compact Open LLMs with Knowledge Graph Reasoning via Reinforcement Learning

Large Language Models (LLMs) demonstrate impressive natural language capabilities but often struggle with knowledge-intensive reasoning tasks. Knowledge Base Question Answering (KBQA), which leverages structured Knowledge Graphs (KGs) exemplifies this challenge due to the need for accurate multi-hop reasoning. Existing approaches typically perform sequential reasoning steps guided by predefined pipelines, restricting flexibility and causing error cascades due to isolated reasoning at each step. To address these limitations, we propose KG-Hopper, a novel Reinforcement Learning (RL) framework that empowers compact open LLMs with the ability to perform integrated multi-hop KG reasoning within a single inference round. Rather than reasoning step-by-step, we train a Reasoning LLM that embeds the entire KG traversal and decision process into a unified ``thinking'' stage, enabling global reasoning over cross-step dependencies and dynamic path exploration with backtracking. Experimental results on eight KG reasoning benchmarks show that KG-Hopper, based on a 7B-parameter LLM, consistently outperforms larger multi-step systems (up to 70B) and achieves competitive performance with proprietary models such as GPT-3.5-Turbo and GPT-4o-mini, while remaining compact, open, and data-efficient. The code is publicly available at: https://github.com/Wangshuaiia/KG-Hopper.

Shuai Wang, Yinan Yu

Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, SE-41296 Gothenburg, Sweden

LLM Reasoning with Graphs Knowledge Graph Question Answering Multi-Hop Reasoning RL for Language Model Reasoning

Mar 22, 2026

When Models Judge Themselves: Unsupervised Self-Evolution for Multimodal Reasoning

Recent progress in multimodal large language models has led to strong performance on reasoning tasks, but these improvements largely rely on high-quality annotated data or teacher-model distillation, both of which are costly and difficult to scale. To address this, we propose an unsupervised self-evolution training framework for multimodal reasoning that achieves stable performance improvements without using human-annotated answers or external reward models. For each input, we sample multiple reasoning trajectories and jointly model their within group structure. We use the Actor's self-consistency signal as a training prior, and introduce a bounded Judge based modulation to continuously reweight trajectories of different quality. We further model the modulated scores as a group level distribution and convert absolute scores into relative advantages within each group, enabling more robust policy updates. Trained with Group Relative Policy Optimization (GRPO) on unlabeled data, our method consistently improves reasoning performance and generalization on five mathematical reasoning benchmarks, offering a scalable path toward self-evolving multimodal models. The code are available at https://github.com/OPPO-Mente-Lab/LLM-Self-Judge.

Zhengxian Wu, Kai Shi, Chuanrui Zhang +10

OPPO AI Center · Tsinghua University · Nanyang Technological University +1

Multimodal Reasoning Self-Training for Language Models RL for Language Model Reasoning

Mar 22, 2026

WIST: Web-Grounded Iterative Self-Play Tree for Domain-Targeted Reasoning Improvement

Recent progress in reinforcement learning with verifiable rewards (RLVR) offers a practical path to self-improvement of language models, but existing methods face a key trade-off: endogenous self-play can drift over iterations, while corpus-grounded approaches rely on curated data environments. We present WIST, a Web-grounded Iterative Self-play Tree framework for domain-targeted reasoning improvement that learns directly from the open web without requiring any pre-arranged domain corpus. WIST incrementally expands a domain tree for exploration, and retrieves and cleans path-consistent web corpus to construct a controllable training environment. It then performs Challenger--Solver self-play with verifiable rewards, and feeds learnability signals back to update node posteriors and guide subsequent exploration through an adaptive curriculum. Across four backbones, WIST consistently improves over the base models and typically outperforms both purely endogenous self-evolution and corpus-grounded self-play baselines, with the Overall gains reaching +9.8 (Qwen3-4B-Base) and +9.7 (OctoThinker-8B). WIST is also domain-steerable, improving Qwen3-8B-Base by +14.79 in medicine and Qwen3-4B-Base by +5.28 on PhyBench. Ablations further confirm the importance of WIST's key components for stable open-web learning. Our Code is available at https://github.com/lfy-123/WIST.

Fangyuan Li, Pengfei Li, Shijie Wang +4

Harbin Institute of Technology · Shanghai Innovation Institute · Shanghai Artificial Intelligence Laboratory

Language Model Self-Improvement RL for Language Model Reasoning Self-Play RL Reinforcement Learning with Verifiable Rewards Curriculum RL

Mar 22, 2026

LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning

We introduce LongCat-Flash-Prover, a flagship 560-billion-parameter open-source Mixture-of- Experts (MoE) model that advances Native Formal Reasoning in Lean4 through agentic tool-integrated reasoning (TIR). We decompose the native formal reasoning task into three independent formal capabilities, i.e., auto-formalization, sketching, and proving. To facilitate these capabilities, we propose a Hybrid-Experts Iteration Framework to expand high-quality task trajectories, including generating a formal statement based on a given informal problem, producing a whole-proof directly from the statement, or a lemma-style sketch. During agentic RL, we present a Hierarchical Importance Sampling Policy Optimization (HisPO) algorithm, which aims to stabilize the MoE model training on such long-horizon tasks. It employs a gradient masking strategy that accounts for the policy staleness and the inherent train-inference engine discrepancies at both sequence and token levels. Additionally, we also incorporate theorem consistency and legality detection mechanisms to eliminate reward hacking issues. Extensive evaluations show that our LongCat-Flash-Prover sets a new state-of-the-art for open-weights models in both auto-formalization and theorem proving. Demonstrating remarkable sample efficiency, it achieves a 97.1% pass rate on MiniF2F-Test using only 72 inference budget per problem. On more challenging benchmarks, it solves 70.8% of ProverBench and 41.5% of PutnamBench with no more than 220 attempts per problem, significantly outperforming existing open-weights baselines.

Jianing Wang, Jianfei Zhang, Qi Guo +24

Meituan LongCat Team

Large Language Model-Guided Theorem Proving Automated Theorem Proving Autoformalization RL for Language Model Reasoning Agentic RL

Mar 21, 2026

RLVR Training of LLMs Does Not Improve Thinking Ability for General QA: Evaluation Method and a Simple Solution

Reinforcement learning from verifiable rewards (RLVR) stimulates the thinking processes of large language models (LLMs), substantially enhancing their reasoning abilities on verifiable tasks. It is often assumed that similar gains should transfer to general question answering (GQA), but this assumption has not been thoroughly validated. To assess whether RLVR automatically improves LLM performance on GQA, we propose a Cross-Generation evaluation framework that measures the quality of intermediate reasoning by feeding the generated thinking context into LLMs of varying capabilities. Our evaluation leads to a discouraging finding: the efficacy of the thinking process on GQA tasks is markedly lower than on verifiable tasks, suggesting that explicit training on GQA remains necessary in addition to training on verifiable tasks. We further observe that direct RL training on GQA is less effective than RLVR. Our hypothesis is that, whereas verifiable tasks demand robust logical chains to obtain high rewards, GQA tasks often admit shortcuts to high rewards without cultivating high-quality thinking. To avoid possible shortcuts, we introduce a simple method, Separated Thinking And Response Training (START), which first trains only the thinking process, using rewards defined on the final answer. We show that START improves both the quality of thinking and the final answer across several GQA benchmarks and RL algorithms.

Kaiyuan Li, Jing-Cheng Pang, Yang Yu

National Key Laboratory for Novel Software Technology & School of Artificial Intelligence, Nanjing University, China · Polixir.ai, China · Huawei Technologies Co., Ltd., China

Language Model Reasoning Evaluation RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Question Answering LLM Evaluation

Mar 20, 2026

Experience is the Best Teacher: Motivating Effective Exploration in Reinforcement Learning for LLMs

Reinforcement Learning (RL) with rubric-based rewards has recently shown remarkable progress in enhancing general reasoning capabilities of Large Language Models (LLMs), yet still suffers from ineffective exploration confined to curent policy distribution. In fact, RL optimization can be viewed as steering the policy toward an ideal distribution that maximizes the rewards, while effective exploration should align efforts with desired target. Leveraging this insight, we propose HeRL, a Hindsight experience guided Reinforcement Learning framework to bootstrap effective exploration by explicitly telling LLMs the desired behaviors specified in rewards. Concretely, HeRL treats failed trajectories along with their unmet rubrics as hindsight experience, which serves as in-context guidance for the policy to explore desired responses beyond its current distribution. Additionally, we introduce a bonus reward to incentivize responses with greater potential for improvement under such guidance. HeRL facilitates effective learning from desired high quality samples without repeated trial-and-error from scratch, yielding a more accurate estimation of the expected gradient theoretically. Extensive experiments across various benchmarks demonstrate that HeRL achieves superior performance gains over baselines, and can further benefit from experience guided self-improvement at test time. Our code is available at https://github.com/sikelifei/HeRL.

Wenjian Zhang, Kongcheng Zhang, Jiaxin Qi +2

Dalian University of Technology · Zhejiang University · Chinese Academy of Sciences

Hindsight Experience Replay RL for Language Model Reasoning RL Exploration Rubric-Based RL In-Context RL Reward Design for RL

Mar 20, 2026

Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States

Reinforcement learning (RL) has become a standard paradigm for post-training and aligning Large Language Models (LLMs), yet recent evidence suggests it faces a persistent "capability ceiling": unlike classical RL systems that discover novel strategies, RL for LLMs often acts as a mere refiner of patterns already latent in pre-trained weights. In this work, we identify a fundamental structural bottleneck: while classical RL relies on compact, informative Markov states, current LLM post-training formulations are tethered to an ever-expanding history of actions. We revisit a classical principle long central to RL yet absent from LLM post-training: explicit Markov states. Theoretically, we provide rigorous guarantees demonstrating that leveraging estimated Markov states can significantly reduce sample complexity. Empirically, we show that introducing Markov states consistently breaks the performance boundaries of standard RL post-training across a suite of complex logic puzzles. Our findings suggest that moving beyond "history-as-state" modeling in favor of structured Markovian representations is essential for unlocking open-ended discovery and genuinely new reasoning capabilities in Generative AI.

Yurun Yuan, Tengyang Xie

UW-Madison

RL for Language Model Reasoning RL Post-Training Sample-Efficient RL

Mar 20, 2026

What If Consensus Lies? Selective-Complementary Reinforcement Learning at Test Time

Test-Time Reinforcement Learning (TTRL) enables Large Language Models (LLMs) to enhance reasoning capabilities on unlabeled test streams by deriving pseudo-rewards from majority voting consensus. However, existing TTRL methods rely exclusively on positive pseudo-labeling strategies. Such reliance becomes vulnerable under challenging scenarios where answer distributions are highly dispersed, resulting in weak consensus that inadvertently reinforces incorrect trajectories as supervision signals. In this paper, we propose SCRL (Selective-Complementary Reinforcement Learning), a robust test-time reinforcement learning framework that effectively mitigates label noise amplification. SCRL develops Selective Positive Pseudo-Labeling, which enforces strict consensus criteria to filter unreliable majorities. Complementarily, SCRL introduces Entropy-Gated Negative Pseudo-Labeling, the first negative supervision mechanism in TTRL, to reliably prune incorrect trajectories based on generation uncertainty. Extensive experiments on multiple reasoning benchmarks demonstrate that SCRL achieves substantial improvements over baselines, while maintaining robust generalization and training stability under constrained rollout budgets. Our code is available at https://github.com/Jasper-Yan/SCRL.

Dong Yan, Jian Liang, Yanbo Wang +3

School of Artificial Intelligence, University of Chinese Academy of Sciences · NLPR & MAIS, Institute of Automation, Chinese Academy of Sciences · Nanjing University

RL for Language Model Reasoning Test-Time RL Pseudo-Labeling Learning with Noisy Labels

Mar 20, 2026

FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Chiyu Ma, Shuo Yang, Kexin Huang +7

Qwen Pilot Team, Alibaba Group

RL for Language Model Reasoning RL for Language Models LLM Reasoning

Mar 20, 2026

EvidenceRL: Reinforcing Evidence Consistency for Trustworthy Language Models

Large Language Models (LLMs) are fluent but prone to hallucinations, producing answers that appear plausible yet are unsupported by available evidence. This failure is especially problematic in high-stakes domains where decisions must be justified by verifiable information. We introduce EvidenceRL, a reinforcement learning framework that enforces evidence adherence during training. EvidenceRL scores candidate responses for grounding (entailment with retrieved evidence and context) and correctness (agreement with reference answers) and optimizes the generator using Group Relative Policy Optimization (GRPO). We evaluate across two high-stakes domains, cardiac diagnosis and legal reasoning, where EvidenceRL consistently improves evidence grounding and faithfulness without sacrificing task accuracy. On cardiac diagnosis, F1@3 increases from 37.0 to 54.5 on Llama-3.2-3B while grounding (

G_{\max}@3

) rises from 47.6 to 78.2; hallucinations drop nearly 5

\times

and evidence-supported diagnoses increase from 31.8% to 61.6%. On legal reasoning, EvidenceRL raises Faithfulness from 32.8% to 67.6% on Llama-3.1-8B, demonstrating consistent behavioral change across domains. Our code is open-sourced at https://github.com/Wizaaard/EvidenceRL.git.

J. Ben Tamo, Yuxing Lu, Benoit L. Marteau +2

Georgia Institute of Technology · Pekin University

LLM Hallucination Mitigation LLM Grounding Faithfulness of Language Model Explanations RL for Language Model Reasoning

Mar 19, 2026

Adaptive Layerwise Perturbation: Unifying Off-Policy Corrections for LLM RL

Off-policy problems such as policy staleness and training--inference mismatch have become a major bottleneck for training stability and further exploration in LLM RL. The distribution gap between the inference and updated policies grows because of the techniques to enhance inference efficiency, leading to heavy-tailed importance ratios. Heavy-tailed ratios arise when the policy is locally sharp, which further inflates gradients and can push updates outside the trust region. To address this, we propose Adaptive Layerwise Perturbation (ALP), which injects small learnable perturbations into the input hidden states of each layer during updates and uses the resulting perturbed policy as the numerator of the importance ratio against the unchanged inference policy in the objective. Intuitively, by adding controlled noise to intermediate representations, ALP prevents the updated policy from deviating too sharply from the inference policy and enlarges the policy family to cover inference-time mismatch noise. Hence, the flattened distribution can naturally tighten the gap between the updated and inference policies and reduce the tail of importance ratios, thus maintaining training stability. This is further validated empirically. Experiments on single-turn math and multi-turn tool-integrated reasoning tasks show that ALP not only improves final performance, but also avoids blow-up in the importance-ratio tail and KL spikes during iterative training, along with boosted exploration. Ablations show that representation-level perturbations across all layers are most effective, substantially outperforming partial-layer and logits-only variants.

Chenlu Ye, Xuanchang Zhang, Yifan Hao +6

University of Illinois Urbana-Champaign · Amazon

Importance Sampling for RL RL for Language Models Reinforcement Learning Off-Policy RL RL for Language Model Reasoning Policy Optimization

Mar 19, 2026

Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation

We introduce Nemotron-Cascade 2, an open 30B MoE model with 3B activated parameters that delivers best-in-class reasoning and strong agentic capabilities. Despite its compact size, its mathematical and coding reasoning performance approaches that of frontier open models. It is the second open-weight LLM, after DeepSeekV3.2-Speciale-671B-A37B, to achieve Gold Medal-level performance in the 2025 International Mathematical Olympiad (IMO), the International Olympiad in Informatics (IOI), and the ICPC World Finals, demonstrating remarkably high intelligence density with 20x fewer parameters. In contrast to Nemotron-Cascade 1, the key technical advancements are as follows. After SFT on a meticulously curated dataset, we substantially expand Cascade RL to cover a much broader spectrum of reasoning and agentic domains. Furthermore, we introduce multi-domain on-policy distillation from the strongest intermediate teacher models for each domain throughout the Cascade RL process, allowing us to efficiently recover benchmark regressions and sustain strong performance gains along the way. We release the collection of model checkpoint and training data.

Zhuolin Yang, Zihan Liu, Yang Chen +14

RL for Language Model Reasoning RL for LLM Agents Reinforcement Learning Language Model Distillation On-Policy Distillation

Mar 19, 2026

MoRI: Learning Motivation-Grounded Reasoning for Scientific Ideation in Large Language Models

Scientific ideation aims to propose novel solutions within a given scientific context. Existing LLM-based agentic approaches emulate human research workflows, yet inadequately model scientific reasoning, resulting in surface-level conceptual recombinations that lack technical depth and scientific grounding. To address this issue, we propose MoRI (Motivation-grounded Reasoning for Scientific Ideation), a framework that enables LLMs to explicitly learn the reasoning process from research motivations to methodologies. The base LLM is initialized via supervised fine-tuning to generate a research motivation from a given context, and is subsequently trained under a composite reinforcement learning reward that approximates scientific rigor: (1) entropy-aware information gain encourages the model to uncover and elaborate high-complexity technical details grounded in ground-truth methodologies, and (2) contrastive semantic gain constrains the reasoning trajectory to remain conceptually aligned with scientifically valid solutions. Empirical results show that MoRI consistently outperforms strong commercial LLMs and complex agentic baselines across multiple dimensions, including novelty, technical rigor, and feasibility. The code is available on GitHub.

Chenyang Gu, Jiahao Cheng, Meicong Zhang +3

School of Economics and Management, East China Normal University

Scientific Reasoning in Language Models Large Language Model-Guided Scientific Discovery Scientific Hypothesis Generation RL for Language Model Reasoning

Mar 19, 2026

Context Bootstrapped Reinforcement Learning

Reinforcement Learning from Verifiable Rewards (RLVR) suffers from exploration inefficiency, where models struggle to generate successful rollouts, resulting in minimal learning signal. This challenge is particularly severe for tasks that require the acquisition of novel reasoning patterns or domain-specific knowledge. To address this, we propose Context Bootstrapped Reinforcement Learning (CBRL), which augments RLVR training by stochastically prepending few-shot demonstrations to training prompts. The injection probability follows a curriculum that starts high to bootstrap early exploration, then anneals to zero so the model must ultimately succeed without assistance. This forces the policy to internalize reasoning patterns from the demonstrations rather than relying on them at test time. We validate CBRL across two model families and five Reasoning Gym tasks. Our results demonstrate that CBRL consistently improves success rate, provides better exploration efficiency, and is algorithm-agnostic. We further demonstrate CBRL's practical applicability on Q, a domain-specific programming language that diverges significantly from mainstream language conventions.

Saaket Agashe, Jayanth Srinivasa, Gaowen Liu +2

University of California, Santa Barbara · Cisco Research

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards RL for Code Generation Curriculum RL

Mar 19, 2026

Are complicated loss functions necessary for teaching LLMs to reason?

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Gabriele Carrino, Andrea Sassella, Nicolo Brunello +2

DEIB, Politecnico di Milano Via Ponzio 34/5, 20133, Milano (MI), Italy

RL for Language Model Reasoning Group Relative Policy Optimization RL Post-Training Reinforcement Learning LLM Mathematical Reasoning

Mar 19, 2026

Thinking with Constructions: A Benchmark and Policy Optimization for Visual-Text Interleaved Geometric Reasoning

Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are largely confined to passive inference with static diagrams, lacking the strategic knowledge of when and how to construct effective visual aids. To address this, we present a framework for Visual-Text Interleaved Chain-of-Thought. We first introduce GeoAux-Bench, the first benchmark comprising 4,334 geometry problems that aligns textual construction steps with ground-truth visual updates. Our pilot study reveals two critical insights: (1) interleaved visual-textual aids outperform single-modality counterparts, which cannot losslessly capture geometric synergy; and (2) valid constructions act as entropy reducers, strongly correlating with reduced reasoning perplexity. Building on these findings, we propose Action Applicability Policy Optimization (A2PO), a reinforcement learning paradigm for mastering strategic construction. A2PO employs Adaptive Reward Shaping to regulate the timing and quality of visual aids via counterfactual sampling to distinguish necessary from redundant constructions. Experiments demonstrate our approach enables MLLMs to leverage selective auxiliary constructions, yielding a 3.51% gain over strong baselines. Code and data are available on GitHub.

Haokun Zhao, Wanshi Xu, Haidong Yuan +3

College of Computer Science and Artificial Intelligence, Fudan University · School of ECE, Peking University · School of Software and Microelectronics, Peking University +1

Visual Spatial Reasoning Mathematical Reasoning Multimodal CoT Reasoning Mathematical Reasoning Benchmarks RL for Language Model Reasoning

Mar 19, 2026

Balancing the Reasoning Load: Difficulty-Differentiated Policy Optimization with Length Redistribution for Efficient and Robust Reinforcement Learning

Large Reasoning Models (LRMs) have shown exceptional reasoning capabilities, but they also suffer from the issue of overthinking, often generating excessively long and redundant answers. For problems that exceed the model's capabilities, LRMs tend to exhibit the overconfidence phenomenon, generating overly short but incorrect answers, which may contribute to suboptimal performance. To address these issues, we propose Difficulty-Differentiated Policy Optimization (DDPO), an efficient reinforcement learning algorithm that optimizes simple and complex tasks separately based on the overconfidence phenomenon. Specifically, it reduces the output length for simple tasks without compromising accuracy, while for complex tasks, it expands the exploration space to improve performance. We further derive the theoretical conditions for maximizing expected accuracy, which require the length distribution to closely approximate the optimal length and be as concentrated as possible. Based on these conditions, we propose using the difficulty-level average as a well-founded reference for length optimization. Extensive experiments on both in-domain and out-of-domain benchmarks validate the superiority and effectiveness of DDPO. Compared to GRPO, DDPO reduces the average answer length by 12% while improving accuracy by 1.85% across multiple benchmarks, achieving a better trade-off between accuracy and length. The code is available at https://github.com/Yinan-Xia/DDPO.

Yinan Xia, Haotian Zhang, Huiming Wang

Tianjin University · Kuaishou Technology

RL for Language Model Reasoning Efficient Language Model Reasoning RL Post-Training Overthinking in Language Models

Mar 19, 2026

Discounted Beta-Bernoulli Reward Estimation for Sample-Efficient Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective post-training paradigm for improving the reasoning capabilities of large language models. However, existing group-based RLVR methods often suffer from severe sample inefficiency. This inefficiency stems from reliance on point estimation of rewards from a small number of rollouts, leading to high estimation variance, variance collapse, and ineffective utilization of generated responses. In this work, we reformulate RLVR from a statistical estimation perspective by modeling rewards as samples drawn from a policy-induced distribution and casting advantage computation as the problem of estimating the reward distribution from finite data. Building on this view, we propose Discounted Beta-Bernoulli (DBB) reward estimation, which leverages historical reward statistics for the non-stationary distribution. Although biased, the resulting estimator exhibits reduced and stable variance, theoretically avoids estimated variance collapse, and achieves lower mean squared error than standard point estimation. Extensive experiments across six in-distribution and three out-of-distribution reasoning benchmarks demonstrate that GRPO with DBB consistently outperforms naive GRPO, achieving average Acc@8 improvements of 3.22/2.42 points in-distribution and 12.49/6.92 points out-of-distribution on the 1.7B and 8B models, respectively, without additional computational cost or memory usage.

Haechan Kim, Soohyun Ryu, Gyouk Chu +2

Kim Jaechul Graduate School of AI, KAIST, Daejeon, South Korea · KRAFTON, Seoul, South Korea · AITRICS, Seoul, South Korea

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Sample-Efficient RL

Mar 19, 2026

PowerFlow: Unlocking the Dual Nature of LLMs via Principled Distribution Matching

Unsupervised Reinforcement Learning from Internal Feedback (RLIF) has emerged as a promising paradigm for eliciting the latent capabilities of Large Language Models (LLMs) without external supervision. However, current methods rely on heuristic intrinsic rewards, which often lack a well-defined theoretical optimization target and are prone to degenerative biases. In this work, we introduce PowerFlow, a principled framework that reformulates unsupervised fine-tuning as a distribution matching problem. By casting GFlowNet as an amortized variational sampler for unnormalized densities, we propose a length-aware Trajectory-Balance objective that explicitly neutralizes the structural length biases inherent in autoregressive generation. By targeting

α

-power distributions, PowerFlow enables the directional elicitation of the dual nature of LLMs: sharpening the distribution (

α> 1

) to intensify logical reasoning, or flattening it (

α< 1

) to unlock expressive creativity. Extensive experiments demonstrate that PowerFlow consistently outperforms existing RLIF methods, matching or even exceeding supervised GRPO. Furthermore, by mitigating over-sharpening in aligned models, our approach achieves simultaneous gains in diversity and quality, shifting the Pareto frontier in creative tasks.

Ruishuo Chen, Yu Chen, Zhuoran Li +1

Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

RL for Language Models Reinforcement Learning RL for Language Model Reasoning Text Generation Generative Flow Networks

Mar 18, 2026

Learning to Reason with Curriculum I: Provable Benefits of Autocurriculum

Chain-of-thought reasoning, where language models expend additional computation by producing thinking tokens prior to final responses, has driven significant advances in model capabilities. However, training these reasoning models is extremely costly in terms of both data and compute, as it involves collecting long traces of reasoning behavior from humans or synthetic generators and further post-training the model via reinforcement learning. Are these costs fundamental, or can they be reduced through better algorithmic design? We show that autocurriculum, where the model uses its own performance to decide which problems to focus training on, provably improves upon standard training recipes for both supervised fine-tuning (SFT) and reinforcement learning (RL). For SFT, we show that autocurriculum requires exponentially fewer reasoning demonstrations than non-adaptive fine-tuning, by focusing teacher supervision on prompts where the current model struggles. For RL fine-tuning, autocurriculum decouples the computational cost from the quality of the reference model, reducing the latter to a burn-in cost that is nearly independent of the target accuracy. These improvements arise purely from adaptive data selection, drawing on classical techniques from boosting and learning from counterexamples, and requiring no assumption on the distribution or difficulty of prompts.

Nived Rajaraman, Audrey Huang, Miro Dudik +3

Microsoft Research · University of Illinois Urbana Champaign

Efficient Language Model Training Curriculum RL RL for Language Model Reasoning RL Fine-Tuning

Mar 18, 2026

MolRGen: A Training and Evaluation Setting for De Novo Molecular Generation with Reasonning Models

Recent reasoning-based large language models have shown strong performance on tasks with verifiable outcomes, but their use in de novo molecular generation remains limited by the lack of training environments where rewards can be computed without reference molecules. We introduce MolRGen, a benchmark and molecular verifier for training and evaluating reasoning LLMs on de novo molecular generation. MolRGen contains approximately 4,500 protein-pocket targets, resulting in 50k multi-objective optimization prompts combining docking scores with molecular properties such as QED, synthetic accessibility, logP, and physicochemical descriptors. Unlike caption-based generation or molecule-editing benchmarks, MolRGen evaluates molecules proposed from scratch by computing rewards at generation time. We benchmark general-purpose and chemistry-specialized open-source LLMs and introduce a diversity-aware top-k metric to measure whether models can generate a diverse set of high-scoring molecules. Finally, we use the verifier to fine-tune a 128B LLM with GRPO, showing improved performance, at the cost of a diversity-exploitation trade-off. MolRGen provides a scalable testbed for studying verifier-based reasoning and reinforcement learning in molecular design.

Philippe Formont, Maxime Darrin, Ismail Ben Ayed +1

Universit´e Paris-Saclay · ´ETS Montr´eal · ILLS – International Laboratory on Learning Systems +4

Molecular Generation Molecule Design Molecular Optimization RL for Language Model Reasoning

Mar 18, 2026

CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution

Label-free reinforcement learning enables large language models to improve reasoning capabilities without ground-truth supervision, typically by treating majority-voted answers as pseudo-labels. However, we identify a critical failure mode: as training maximizes self-consistency, output diversity collapses, causing the model to confidently reinforce systematic errors that evade detection. We term this the consensus trap. To escape it, we propose CoVerRL, a framework where a single model alternates between generator and verifier roles, with each capability bootstrapping the other. Majority voting provides noisy but informative supervision for training the verifier, while the improving verifier progressively filters self-consistent errors from pseudo-labels. This co-evolution creates a virtuous cycle that maintains high reward accuracy throughout training. Experiments across Qwen and Llama model families demonstrate that CoVerRL outperforms label-free baselines by 4.7-5.9% on mathematical reasoning benchmarks. Moreover, self-verification accuracy improves from around 55% to over 85%, confirming that both capabilities genuinely co-evolve.

Teng Pan, Yuchen Yan, Zixuan Wang +6

Zhejiang University · Baidu Inc.

Language Model Self-Verification RL for Language Model Reasoning LLM Reasoning Self-Training for Language Models Self-Consistency in Language Models

Mar 18, 2026

TRiMS: Real-Time Tracking of Minimal Sufficient Length for Efficient Reasoning via RL

Large language models achieve breakthroughs in complex reasoning via long chain-of-thought sequences. However, this often leads to severe reasoning inflation, causing substantial computational redundancy. To maximize Intelligence per Token, we introduce a theoretical metric, MSL-Minimal Sufficient Length. MSL rigorously characterizes the shortest reasoning length that preserves answer correctness. We provide a recursive definition based on independently sampled sequences and prove the existence of its limit, establishing the first measurable lower bound for reasoning-chain compression. Building on an analysis of mainstream CoT compression strategies, we identify key structural factors enabling a model to approach MSL. Based on these insights, we propose TRiMS which employs the GRPO algorithm in conjunction with MSL-based estimation during training, while mitigating instabilities during the training process through dynamic batch aggregation and advantage computation using batch-level standard deviation. TRiMS achieves over 80% CoT token reduction with a minor accuracy boost across all benchmarks.

Tingcheng Bian, Jinchang Luo, Mingquan Cheng +5

Baidu Inc. · Shenzhen University · Harbin Institute of Technology

Efficient Language Model Reasoning CoT Compression RL for Language Model Reasoning

Mar 18, 2026

InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning

Large Language Models (LLMs) with extended reasoning capabilities often generate verbose and redundant reasoning traces, incurring unnecessary computational cost. While existing reinforcement learning approaches address this by optimizing final response length, they neglect the quality of intermediate reasoning steps, leaving models vulnerable to reward hacking. We argue that verbosity is not merely a length problem, but a symptom of poor intermediate reasoning quality. To investigate this, we conduct an empirical study tracking the per-token predictive entropy of large reasoning models across reasoning trajectories. We find that high-quality reasoning traces exhibit two consistent properties: low uncertainty convergence and fast uncertainty descent. These findings suggest that high-quality reasoning traces are informationally dense, that is, reasoning steps contribute to reaching a low uncertainty level relative to the total reasoning length. Motivated by this, we propose InfoDensity, a reward framework for RL training that captures both properties through a single suffix-max envelope of the entropy trajectory, weighted by a length scaling term that favors achieving equivalent quality more concisely. Experiments on mathematical and general reasoning benchmarks demonstrate that InfoDensity outperforms state-of-the-art baselines on the accuracy-efficiency trade-off.

Chengwei Wei, Jung-jae Kim, Longyin Zhang +2

Institute for Infocomm Research (I2R), A*STAR, Singapore · Centre for Frontier AI Research (CFAR), A*STAR, Singapore

Efficient Language Model Reasoning RL for Language Model Reasoning Reward Shaping

Mar 18, 2026

Contrastive Reasoning Alignment: Reinforcement Learning from Hidden Representations

We propose CRAFT, a red-teaming alignment framework that leverages model reasoning capabilities and hidden representations to improve robustness against jailbreak attacks. Unlike prior defenses that operate primarily at the output level, CRAFT aligns large reasoning models to generate safety-aware reasoning traces by explicitly optimizing objectives defined over the hidden state space. Methodologically, CRAFT integrates contrastive representation learning with reinforcement learning to separate safe and unsafe reasoning trajectories, yielding a latent-space geometry that supports robust, reasoning-level safety alignment. Theoretically, we show that incorporating latent-textual consistency into GRPO eliminates superficially aligned policies by ruling them out as local optima. Empirically, we evaluate CRAFT on multiple safety benchmarks using two strong reasoning models, Qwen3-4B-Thinking and R1-Distill-Llama-8B, where it consistently outperforms state-of-the-art defenses such as IPO and SafeKey. Notably, CRAFT delivers an average 79.0% improvement in reasoning safety and 87.7% improvement in final-response safety over the base models, demonstrating the effectiveness of hidden-space reasoning alignment.

Haozheng Luo, Yimin Wang, Jiahao Yu +2

Northwestern University · University of Michigan · Illinois Institute of Technology

LLM Safety Alignment Jailbreak Defense RL for Language Model Reasoning

Mar 17, 2026

PRISM: Demystifying Retention and Interaction in Mid-Training

We present PRISM, a comprehensive empirical study of mid-training design choices for large language models. Through controlled experiments across seven base models spanning four families (Granite, LLaMA, Mistral, Nemotron-H), two architecture types (dense Transformer and attention-Mamba hybrid), and scales from 3B to 24B parameters, we show that mid-training on approximately 27B high-quality tokens yields consistent gains of +15 to +40 points on math, +5 to +12 points on code, and +6 to +13 points on science benchmarks while preserving general performance. The full PRISM to RL pipeline improves macro-average across six reasoning benchmarks from under 12 to 29-42 (a 3-4x improvement), whereas RL applied directly to most of the base models remains substantially less effective, with AIME scores near zero. Data composition matters most at mid-training, not RL: including science data during mid-training unlocks +17 to +28 point GPQA-Diamond gains during RL, while changing the RL mix produces less than 2 point differences. Mechanistically, mid-training densely restructures over 90% of model weights, while RL makes sparse, front-loaded refinements to approximately 5% of parameters. Representation analysis (CKA) confirms that RL consistently preserves mid-training's representational geometry (over 0.998 CKA) across architectures. Crucially, RL applies identical weight changes regardless of starting point, yet only succeeds on mid-trained models, consistent with mid-training placing the model in a configuration from which RL can effectively improve performance. Our results demonstrate that retention-aware mid-training is highly effective for reliable reasoning enhancement and provide practical guidance for designing robust mid-training pipelines.

Bharat Runwal, Ashish Agrawal, Anurag Roy +1

IBM Research, MIT-IBM Watson AI Lab

LLM Training Scientific Reasoning in Language Models RL for Language Model Reasoning