RL for Language Model Reasoning

RL: Reinforcement Learning

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91 papers in the last four weeks, up 176% on the four weeks before. 0.9% of all new papers.

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Sep 29, 2026cs.LG

Inducing Process Supervision from Outcome-Only Reinforcement Learning

Process reward models (PRMs) have become a key component for LLMs, as their step-level feedback supports both post-training and test-time reasoning. However, training strong PRMs remains costly: human step annotation is difficult to scale, while Monte Carlo estimation is computationally expensive and can drift from the intrinsic correctness of steps. To get effective PRMs at low cost, we introduce TIPS (Thinking-Induced Process Supervision), an outcome-only reinforcement learning (RL) framework for training generative PRMs. In TIPS, the model generates a chain-of-thought (CoT) followed by step-level labels and an outcome label. The reward depends solely on whether the predicted outcome matches the ground truth, and the resulting group-relative advantage is used to optimize the entire generated response. Intuitively, when checking intermediate steps helps determine the outcome, more accurate checks can lead to better outcome judgments and higher rewards. Outcome-only RL can therefore reinforce step-level verification without explicit process supervision. We validate the effectiveness of TIPS across math and agent benchmarks and four backbone families. Notably, TIPS-Qwen3-4B-Thinking-2507 reaches 85.2 F1 on ProcessBench with only 3.2K outcome-labeled trajectories, surpassing all evaluated trained PRMs and strong prompt-only judges such as GPT-5.4-Instruct and Claude-4.7-Opus, while still trailing o1-mini. Code and data are available at https://github.com/RUCBM/TIPS.

Shengda Fan, Xin Cong, Zhong Zhang +2

Renmin University of China · Tsinghua University · University of Electronic Science and Technology of China +1

Reinforcement Learning Process Reward Models RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards

Sep 29, 2026cs.LG

SERA: Scale-Equalized Rollout Allocation for Maximum Likelihood Reinforcement Learning

Maximum Likelihood Reinforcement Learning (MaxRL) targets prompt-wise log-success and has shown strong performance on reasoning tasks. Under finite rollout budgets, however, the estimator used by MaxRL attenuates each prompt's likelihood gradient by a factor that depends on its success probability and rollout count. Under uniform rollout allocation, the common rollout count fails to compensate for success-dependent attenuation, leaving low-success prompts more strongly attenuated and distorting their relative contributions to the expected aggregate gradient. We introduce SERA (Scale-Equalized Rollout Allocation), which redistributes a fixed rollout budget to approximately equalize these finite-rollout scaling factors. Building on our theoretical analysis of how finite rollouts distort prompt-wise likelihood gradients, we formulate the allocation as a fixed-budget max--min problem, derive a waterline solution to its continuous relaxation, and introduce a multiplicity correction to remove the additional prompt weighting induced by heterogeneous rollout counts. Experiments show stronger alignment with exact likelihood gradients in a controlled ImageNet setting and improved multi-sample solution coverage over MaxRL on maze navigation and mathematical reasoning under matched training rollout budgets.

Zihao Chen, Fanxiang Xiong, Hongran Ren +6

Harbin Institute of Technology, Shenzhen · The Chinese University of Hong Kong, Shenzhen · Nanyang Technological University

Reinforcement Learning RL for Language Model Reasoning Sample-Efficient RL

Sep 28, 2026cs.AI

Towards Mitigating Deceptive Safety Alignment in Large Reasoning Models

Large Reasoning Models (LRMs) are commonly trained with reinforcement learning (RL) to improve their generation of chain-of-thought (CoT) reasoning before producing final answers. However, RL rewards are typically assigned based on final answers, providing little or no direct supervision over intermediate reasoning. This can lead to deceptive safety alignment, where the reasoning trace and final answer convey inconsistent safety signals. To systematically investigate this phenomenon, we introduce DSAR (Deceptive Safety Alignment Rate), a metric that jointly assesses reasoning traces and final answers to quantify their safety inconsistency. Across multiple LRMs and benchmarks, we find that deceptive safety alignment is pervasive under standard prompting conditions and is substantially amplified under prefilling attacks. We further provide a hidden representation analysis showing that models exhibit stronger safety discrimination at the final-answer stage than during intermediate reasoning. To close this gap, we propose SARA (Safety-Aware Reasoning Alignment), an RL-based method that rewards both safety-aware reasoning and safe final answers, encouraging early harmful intent recognition and enforcing reasoning-answer consistency. Experiments show that SARA significantly mitigates deceptive safety alignment under both standard and adversarial settings while preserving helpfulness and utility. Code is available at https://github.com/xzhou98/SARA.

Xiangyu Zhou, Saleh Zare Zade, Rafi Ibn Sultan +2

Wayne State University

Language Model Safety Evaluation Deception in Language Models RL for Language Model Reasoning LLM Safety Alignment Large Reasoning Models

Sep 28, 2026cs.LG

An RL View of OPD: Least Square Policy Distillation for Sample-Efficient LLM Reasoning

We study on-policy distillation (OPD) through the lens of reinforcement learning, establishing a connection between the reverse-KL objective in OPD and KL-regularized policy optimization. Building on this connection, we introduce Least-Square Policy Distillation (LSPD), an RL-inspired framework that brings optimistic exploration and off-policy data reuse from value-based RL into policy distillation. LSPD preserves policy diversity through exploration while improving rollout efficiency by repeatedly learning from previously collected trajectories. Our theoretical analysis connects LSPD to optimistic value-based learning and shows that its idealized formulation achieves a sharp

\tilde{\mathcal O}(\log K)

regret bound under online exploration. Empirically, LSPD consistently outperforms existing distillation baselines across six mathematical reasoning benchmarks and diverse teacher-student settings, with average gains of +1.59 points in Avg@16. Remarkably, through Pass@k evaluations up to k=64, we found that LSPD better preserves policy diversity by achieving stronger performance as k grows. Its fully off-policy variant achieves comparable performance to vanilla OPD using only the first 25% of rollout batches. Together, these results provide an RL perspective on OPD that offers both a principled interpretation and a practical route toward more effective and rollout-efficient language model distillation.

Shangzhe Li, Yuxiao Yang, Tianrun Yu +4

University of North Carolina at Chapel Hill · Brigham Young University · NVIDIA

RL for Language Model Reasoning Language Model Distillation On-Policy Distillation Knowledge Distillation

Sep 28, 2026cs.LG

Frontier Learning: Training LLM Reasoners at the Edge of Capability

Reinforcement Learning-based post-training of Large Language Models (LLM) has been successfully applied to improve their reasoning capabilities. Existing pipelines primarily finetune LLMs on a fixed pool of problems specified prior to training using the GRPO loss. This is fundamentally limiting, as learning signal arises only when policy rollouts mix successes and failures, causing the useful portion of any fixed pool to quickly become stale as the model improves. To address this, we propose frontier learning, an open-ended post-training approach in which procedural generators are used online to continually produce informative training problems. It treats the generator's task-specific parameters as a search space and uses a regret signal to prioritize and explore frontier difficulty levels in order to focus training at the edge of the model's evolving reasoning capabilities. Across several reasoning tasks and model families, our approach consistently achieves higher relative gains over fixed-pool baselines, demonstrating that effective post-training requires not only selecting useful problems, but continually generating them at the edge of capability.

Robin Faro, Shyam Sundhar Ramesh, Ilija Bogunovic +1

University College London London, UK · University of Basel Basel, Switzerland

RL for Language Model Reasoning LLM Post-Training

Sep 28, 2026cs.LG

MaPP: A Unified Marginalized Posterior-Predictive Framework for Data-Efficient RLVR

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models but incurs substantial costs from rollouts and policy updates. Online prompt selection improves efficiency by using per-prompt Bayesian posteriors to predict difficulty and prioritize informative prompts. However, existing methods overlook how reliably learning signals are extracted from sampled responses. In GRPO, a response's advantage depends on both its own outcome and the randomly sampled outcomes of its peers through group normalization. Our theoretical and experimental analyses show that uncertainty in group composition introduces composition noise, a non-vanishing variance component that imposes an irreducible lower bound on gradient estimation error and impairs downstream prompt selection. We propose MaPP (Marginalized Posterior-Predictive), a unified framework for data-efficient RLVR that denoises response-level advantage estimation and improves prompt selection using a shared Beta posterior. For each response, MaPP replaces the standard group-relative advantage with a composition-invariant intrinsic advantage through closed-form Beta-Binomial marginalization. The resulting posterior-predictive estimator has an error that provably diminishes as the posterior concentrates. Using the same posterior, MaPP derives an uncertainty-aware prompt selection score to improve data efficiency without additional rollout cost. Experiments on mathematics, planning, and visual geometry across five model backbones show that MaPP consistently outperforms GRPO and strong selection baselines, achieving up to +2.45 average accuracy improvement over the strongest baseline under the same rollout budget and setting a new state of the art.

Yangyang Ren, Haodong Zhu, Sheng Xu +4

Beihang University · Zhongguancun Academy · Communication University of China +4

Bayesian RL RL for Language Model Reasoning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards

Sep 28, 2026cs.LG

Teach to Learn: Hint Annealing for Self-improving LLM Reasoning

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

Zile Wang, Zijian Li, Haodong Wang +5

The Hong Kong University of Science and Technology · Yuanbao Team, Tencent

Reinforcement Learning Self-Training for Language Models RL for Language Model Reasoning LLM Reasoning

Sep 28, 2026cs.LG

Beyond Verbalized Confidence: Calibrating Reasoners with Differentiable Readouts

Reinforcement learning with verifiable rewards (RLVR) trains reasoning models to produce correct answers, but does not ensure that their stated confidence is calibrated. The resulting models are systematically overconfident. Recent methods train calibration inside the RLVR loop by having the model state a numerical confidence alongside its answer, but they all obtain the confidence by sampling it as text. This choice imposes two costs: a sampled confidence introduces variance and in practice collapses to a handful of distinct values, and sampling makes the confidence non-differentiable, forcing the calibration loss through a scalar reward. We propose CREDO (Confidence REaDOut) to replace sampling with a deterministic readout. While RLVR optimizes correctness, CREDO reads the confidence from a dedicated token pair in the model's output distribution and trains it by differentiable regression. CREDO further turns the trained confidence into a signal for accuracy, weighting rollouts by how far confidence and outcome disagree, so that accuracy and calibration improve together. Across mathematical and code reasoning, CREDO attains the best accuracy and calibration, and the gains extend to abstention and selective prediction.

Chenxiao Fan, Chongming Gao, Gangyi Zhang +8

University of Science and Technology of China · Qwen Business Unit of Alibaba · National University of Singapore

Confidence Estimation in Language Models RL for Language Model Reasoning Language Model Calibration Reinforcement Learning with Verifiable Rewards

Sep 28, 2026cs.AI

Can We Trust the Teacher? Decoupled Credit Direction-Magnitude for Self-Distillation

RLVR provides reliable trajectory-level credit, while OPSD offers dense supervision for token-level credit. This exposes a fundamental coupling when updating step-level credit direction and magnitude with teacher supervision, preventing steps from receiving reliable credit directions and contribution magnitudes, while making both vulnerable to teacher judgment errors and preference variance, as supported by our theoretical analysis. To separate credit direction from its contribution magnitude, we introduce \textit{Decoupled Credit Self-Distillation (DCSD)}, which theoretically decouples credit direction and magnitude into two reliable signals and uses them to calibrate privileged teacher supervision. Specifically, we design belief-margin probing to determine credit direction and marginal information gain to quantify credit magnitude, enabling step-to-token credit assignment for policy optimization. Across 11 benchmarks, DCSD achieves the best overall scores against GRPO, OPSD, RLSD, and RLCSD. Compared with base models, DCSD improves the overall score by 8.45 points on mathematical reasoning and 7.01 points on multimodal reasoning, while correcting the credit direction for 6% of tokens and yielding a 1.5

\times

reduction in token credit magnitude.

Yugu Li, Zehong Cao, Peizhen Li +3

School of CSIT, Adelaide University, Adelaide, SA 5000, Australia · CAIAA, University of North Texas, Denton, TX 76203, USA · School of EECMS, Curtin University, Bentley, WA 6102, Australia +1

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Step-Level Credit Assignment Self-Distillation On-Policy Distillation

Sep 28, 2026cs.CL

Rewarding Novel Deductions: Solver-guided Process Supervision for Logical Reasoning

Logical reasoning remains a major challenge for large language models (LLMs), particularly on structured problems that require precise constraint tracking, consistency preservation, and multi-step deduction. This challenge is especially acute for small-scale LLMs, which are more prone to producing inconsistent, redundant, or brittle reasoning trajectories. Existing approaches for improving logical reasoning largely optimize for final-answer correctness, providing only weak supervision over the intermediate reasoning process. In this work, we propose SPRING: (Solver-guided Process Rewards for Novel LogIcal ReasoNing Step Generation). SPRING uses SMT solver as a training-time verifier of intermediate reasoning steps to provide process-level supervision. It introduces the notion of a novel reasoning step, namely, a step that is logically valid, consistent with the evolving reasoning state, and not already implied by previously accepted non-contradictory deductions. Based on this solver-based assessment, it designs process rewards that encourage novel inferential progress while penalizing contradictory and uninformative reasoning steps. Evaluation across three logical reasoning benchmarks, ZebraLogic, AR-LSAT, and Knights and Knaves, and four LLMs shows that SPRING consistently outperforms base LLMs, outcome-only reward baselines, and Logic-LM. On ZebraLogic, SPRING improves puzzle accuracy by up to 49.71 and 15.43 points over the base LLM and strongest outcome-only baseline, respectively. On AR-LSAT, it improves overall accuracy by up to 64.93 and 12.14 points, respectively. On Knights and Knaves, SPRING achieves up to 93.14 puzzle accuracy and 96.05 person accuracy.

Muhammad Asif Ali, Wenqing Wang, Huan Wang +1

FORTE Lab, Faculty of Science, Information Technology University, Lahore, Pakistan · College of Informatics, Huazhong Agricultural University, Wuhan, China · Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar

RL for Language Model Reasoning Process Supervision LLM Reasoning

Sep 28, 2026cs.AI

GlyphBench: A Playground for Language-Model Reinforcement Learning

We introduce GlyphBench, an environment suite for reinforcement learning (RL) post-training of language-model agents, with over 360 tasks spanning diverse games. GlyphBench renders spatial observations as two-dimensional Unicode grids and connects training, evaluation, and trajectory replay through a unified interface designed to support efficient and reproducible research. We use GlyphBench to study how observation interfaces, reasoning effort, and agent harnesses affect performance, and how RL configurations shape learning dynamics. Our results show that glyph observations outperform native text and pixels in our Craftax experiments, with further gains on several BALROG environments. RL on 100 GlyphBench tasks improves Qwen3.5-4B on held-out Reasoning Gym problems, reaching 63.48% accuracy and outperforming the base model, a math-trained baseline, and a code-trained baseline. These experiments provide empirical evidence that reasoning gains from gameplay can yield stronger transfer than math or code. Together, these results highlight GlyphBench's value as a testbed for systematic research on how language-model agents learn, interact, and generalize.

Roger Creus Castanyer, Marc-Alexandre Côté, Matthew James Sargent +3

Mila - Quebec Artificial Intelligence Institute · Université de Montréal · Vmax

RL Benchmarks RL for Language Models RL for Language Model Reasoning RL for LLM Agents

Sep 27, 2026cs.CL

On the Token Value Inequality in Efficient Reasoning

Chain-of-Thought reasoning has enabled large language models to achieve substantial performance gains on complex tasks. However, these gains come at the cost of dramatically increased token consumption. This raises a fundamental question: is every token in the reasoning trace equally valuable? We present a diagnostic and optimization framework grounded in a key empirical finding: the value of tokens within a CoT reasoning sequence is highly non-uniform, and this non-uniformity can be effectively characterized by token-level log probability signals. We show that normalized log probability helps distinguish core tokens, which carry structural and decisive reasoning content, from redundant tokens, which are exploratory, low-confidence filler that contributes less directly to the final answer. Building on these findings, we formulate the TokenProbe framework around two empirical findings and one claim: findings identify token value inequality first and then establish TokenProbe as a core-token proxy, and the claim introduces an efficient GRPO objective positing that selectively compressing redundant tokens can yield Pareto improvements in the accuracy-token efficiency space. Empirically, our method preserves reasoning quality while reducing the token usage by 76% of the baseline. Under matched reasoning-length budgets, we show that it can even outperform strong flagship baselines like Gemini-3.1-Pro. Homepage: https://runjia.tech/tokenprobe/.

Runjia Zeng, Hang Hua, Yiyang Liu +5

Rochester Institute of Technology · Purdue University · MIT-IBM Watson AI Lab +3

RL for Language Model Reasoning Efficient Language Model Reasoning Efficient Language Model Inference CoT Compression Reasoning Trace Analysis

Sep 27, 2026cs.SE

RAISE: Reinforcing Access Control Policy Synthesis in LLMs via Symbolic Evaluation

Translating natural-language access-control requirements into policies requires careful reasoning about permissions, constraints, and exceptions, and even frontier LLMs often produce policies that violate the intended authorization semantics. We construct CedarInstruct, to our knowledge the first dataset that supports both training and semantic evaluation for formally verifiable Cedar policy synthesis. It contains 5,800 scenarios across 44 domains and 1,408 representing a single synthetic organization, each with a verified target policy and an executable verification plan. On this data we introduce RAISE, which trains policy synthesizers from formal verification in two stages, verified supervised fine-tuning (SFT) followed by a reinforcement learning (RL) stage that learns from verifier signal. We find that SFT succeeds largely by letting models express authorization logic they already have, since untrained models rarely write valid Cedar but often reason correctly when they do. After SFT, how the verifier's information is used matters more than how much of it is used. Of six RL instantiations that consume progressively richer verifier signal, only RAISE-OC improves meaningfully on SFT; it turns failed checks and symbolic counterexamples into guided exploration and learns from the result with off-context GRPO. With about 5.4K verified scenarios and LoRA fine-tuning, RAISE-OC trains Qwen3.5-9B to surpass zero-shot GPT-6 Astra and Claude Opus 5 by 13.33 and 16.26 percentage points in semantic success on held-out scenarios, and training transfers to the independently constructed CedarBench.

Yingming Zhou, Adarsh Vatsa, William Eiers

Stevens Institute of Technology

RL for Language Model Reasoning LLM-Based Program Synthesis Access Control

Sep 27, 2026cs.LG

Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoning

Reinforcement learning with verifiable rewards (RLVR) enhances reasoning in large language models (LLMs) through outcome-level feedback, yet recent approaches to finer-grained credit assignment often require auxiliary models, additional sampling, or privileged information. Although policy entropy provides a readily available signal, prioritizing uncertain positions under both reinforcement and penalization concentrates penalties where failed responses still retain alternatives for recovery, which can suppress opportunities for exploration. To address this, we introduce Entropic Advantage Policy Optimization (EAPO), an entropy-guided credit assignment method that treats success and failure asymmetrically. Specifically, motivated by the observation that success under uncertainty is less repeatable while confident failures tend to recur, EAPO couples normalized policy entropy with the sign of the response advantage to reinforce surprising success and correct repeated failure. It assigns stronger reinforcement to high-entropy decisions in successful responses and stronger penalties to low-entropy decisions in failed responses, while attenuating penalties at uncertain positions to preserve opportunities for recovery. By redistributing the response advantage across tokens, EAPO derives token-level credit directly from existing rollout signals without additional supervision. We validate EAPO on a range of reasoning tasks across both base and reasoning backbones, demonstrating that it achieves the best overall performance. We further show that EAPO promotes more effective exploration, broadening problem coverage and generating more diverse candidate answers.

Woongyeong Yeo, Minki Kang, Chanuk Lee +3

KAIST

RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Maximum Entropy RL Reinforcement Learning with Verifiable Rewards

Sep 27, 2026cs.LG

Selecting Diverse SFT Traces Improves Post-RL Generalization

Verified solutions are not equally useful for preparing reasoning models for reinforcement learning (RL). We present a comprehensive study of route diversity, the variation in the sequences of reasoning steps in supervised fine-tuning (SFT) data, and propose a lightweight, rule-based fingerprint to select for it. From one pool at one budget, with matched training recipes and checkpoints, selecting diverse rather than similar routes improves post-RL problem coverage across puzzles and mathematics, including on problems harder than those seen in either training stage. In synthetic experiments, route-diverse SFT improves OLMo3-7B's pass@8 by 16.9 points on environments held out from SFT. In a single-model condition, where one model writes every candidate, diverse selection gains up to 6.2 points of mean pass@8 across 10 mathematics benchmarks. Pre-RL diagnostics suggest why: diverse SFT can produce both successful and failed attempts on more prompts despite slightly lower mean accuracy, giving group-relative RL more prompts with a learning signal. On 3 open-source corpora, our CPU-only selector, without model calls, outperforms more expensive alternatives in every comparison of mean post-RL performance. These results identify reasoning-route diversity as a practical criterion for selecting SFT data that better prepares models for RL.

Dylan Zhang, Mingyuan Wu, Jinning Li

University of Illinois Urbana-Champaign, work done at Google · Google

Reasoning Diversity RL for Language Model Reasoning Training Data Selection RL Post-Training LLM Reasoning

Sep 27, 2026cs.LG

TGRL: Temperature-Grouped Reinforcement Learning for Efficient Exploration in LLMs

Efficient exploration often remains a central bottleneck in reinforcement learning with verifiable rewards (RLVR). Although temperature control and test-time scaling strategies can increase rollout diversity of large language models (LLMs), they either expand the sample budget at rollout time or leave the benefit of exploration unquantified. To this end, we propose Temperature-Grouped Reinforcement Learning (TGRL), which turns temperature-induced diversity into an explicit training signal. For each prompt, TGRL partitions its rollout group into low- and high-temperature subsets, estimates exploration gain through their reward contrast, and allocates this group-level signal as token-level credit using Jensen--Shannon (JS) divergence between the corresponding temperature-scaled next-token distributions induced by the same logits. Notably, TGRL reaches equivalent accuracy up to 36% faster than strong RLVR baselines without expanding the rollout budget. Across 11 benchmarks from diverse domains, TGRL broadly improves over strong RLVR baselines: it improves the six-benchmark math average by 1.6% at 32B, raises CodeForces rating by 196.7 points and LiveCodeBench Pass@16 by 4.4%, and improves ALFWorld/WebShop success rates by 6.3%/4.9%. Comprehensive ablations and wall-clock analysis confirm the efficacy of all proposed components. Code is available at https://github.com/1229095296/TGRL/tree/main.

Zihan Lin, Xiaohan Wang, Jie Cao +4

University of Chinese Academy of Sciences · Meituan · MAIS&NLPR, Institute of Automation, Chinese Academy of Sciences

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

Sep 27, 2026cs.AI

OpenFC: Learning Verification Policies towards Open-Search Fact Checking

Open-search fact checking is not merely retrieval followed by classification, but a sequential decision problem in which every query, source visit, and stopping decision reshapes the evidence available for verification. Yet existing systems often distribute these decisions across predefined pipelines or separately prompted modules rather than learning them as a unified task-specific policy. We introduce \textbf{OpenFC}, a unified verification-policy training framework that post-trains Qwen3-8B as a compact next-action controller over reasoning, evidence acquisition, and stopping. OpenFC learns this policy in two stages. \textbf{Stepwise-Calibrated Cold Start (SCCS)} uses a strong training-time supervisor to review post-initial reasoning, tool-use, and stopping proposals before execution, producing reliable trajectories for supervised fine-tuning without access to gold verdicts. \textbf{Verification-Aware Reinforcement Learning (VA-RL)} then improves the cold-start policy on unresolved claims through budget-aware tool rewards, label-aware advantage reweighting, and localized response masking. Across six fact-checking benchmarks, OpenFC achieves 70.39% average accuracy and 63.30% macro-F1, the highest overall averages among the evaluated methods. Stage-wise ablations further show that SCCS and VA-RL provide complementary gains, supporting the design of the two-stage training framework. These results position OpenFC as a strong and effective framework for open-search fact-checking. We will open-source our code and release the model checkpoints to support reproducibility.

Xinming Wang, Kaixiang Qiu, Yansong Lin +5

Institute of Automation, Chinese Academy of Sciences · University of Electronic Science and Technology of China · Beijing Institute of Technology +1

RL for Language Model Reasoning Automated Fact-Checking LLM Tool Use

Sep 27, 2026cs.CL

TeacherGRPO: Closing the Capacity Gap in Reasoning Distillation via Teacher Alignment

Reasoning distillation from powerful teacher models to smaller students faces the Gap Curse: as teachers grow more sophisticated, their complex distributions increasingly diverge from what students can approximate, causing performance degradation. Existing mitigation strategies either filter out challenging examples through data selection or introduce weaker intermediate assistant models, inherently compromising supervision coverage or quality. We propose Teacher Alignment, which directly adapts the teacher toward the student's distribution without discarding data or degrading reasoning quality. However, naive alignment through standard knowledge distillation triggers catastrophic collapse of the teacher's reasoning capabilities. To address this, we reformulate teacher alignment as reinforcement learning and introduce TeacherGRPO, built on Group Relative Policy Optimization with two key innovations: (i) Curriculum Selective Alignment applies dual token- and distribution-level curricula to focus rewards on high-signal reasoning gaps while filtering noise from trivial tokens and uncertain tail distributions, and (ii) Importance-Adaptive Length Regularization selectively penalizes verbose redundancy while preserving pedagogically critical reasoning steps. The aligned teacher then distills knowledge to students via standard pipelines. Extensive experiments show TeacherGRPO significantly outperforms baselines across diverse reasoning benchmarks and distillation methods. Our code is available at https://github.com/LzyFischer/TeacherGRPO.

Zhenyu Lei, Zihan Chen, Yaochen Zhu +5

University of Virginia · Netflix · University of Washington +2

Reasoning Distillation RL for Language Model Reasoning Language Model Distillation Teacher-Student Learning

Sep 24, 2026cs.CL

Rufus-Air: An Open LLM Post-Training Recipe

Rufus-Air is an open and reproducible post-training recipe on GLM-4.5-Air-Base (106B-A12B), organized as a serial pipeline of eight stages: SFT, Reasoning RL, Coding RL, Instruction-Following RL, General Agent, Coding Agent, Search Agent, and RLHF. We document the data, reward design, infrastructure, stage order, and stagewise results needed to reproduce the recipe. Stages progress from basic to advanced capabilities and from hard, verifiable rewards to softer judge-based signals. Training builds on open-source components and public data, much of it used as released, without new human annotation or an in-house distillation teacher. Our main findings are that (i) diverse, high-quality SFT establishes a strong capability floor; (ii) difficulty filtering keeps RL prompts within a productive learning range; (iii) reward reliability provides a practical principle for ordering stages; and (iv) infrastructure and engineering choices are part of the recipe, not just an implementation detail. Rufus-Air improves over the official GLM-4.5-Air post-trained release and is competitive with similarly sized open models.

Chia-Yuan Chang, Renyuan Cheng, Rui Feng +19

Amazon

LLM Fine-Tuning RL for Language Model Reasoning RL Post-Training LLM Post-Training RL for LLM Agents

Sep 24, 2026cs.AI

CounterRoute: Self-Routed Reasoning via Hierarchical Counterfactual Credit Assignment

Reasoning-capable language models often produce long chains of thought when direct answers suffice, wasting inference compute. Many dual-mode models leave this choice to users. Automating it is challenging because routing targets evolve with the policy, initial mode preferences destabilize exploration, and sequence-level objectives entangle routing with response learning. We introduce CounterRoute, an online reinforcement-learning framework that jointly learns routing and modeconditioned responses in one shared policy directly from a native dual-mode checkpoint, without method-specific SFT warm-up. Paired current-policy counterfactual rollouts assign cross-mode credit only to the routing token, while within-mode GRPO trains response tokens. A paired-to-self-routed curriculum stabilizes early training with forced rollouts from both modes, then increases self-routed updates to improve autonomous routing. Across nine benchmarks, CounterRoute better balances accuracy and efficiency than heuristic and learned adaptive-routing methods. Relative to always-thinking checkpoints, it improves macro-average accuracy while reducing mean generated tokens by 51% for Qwen3-8B and 41% for Qwen3-14B. On instruction-following and commonsense benchmarks where direct answering is strong, think rates fall as low as 1% while response quality improves. Despite training only on math and instruction following, its routing behavior and response quality generalize to held-out coding, science, knowledge, and commonsense benchmarks.

Ruochen Jiao, Besnik Fetahu, Zhenyu Shi +1

RL for Language Model Reasoning Efficient Language Model Reasoning LLM Routing Credit Assignment Efficient Language Model Inference Counterfactual Credit Assignment+1

Sep 23, 2026cs.LG

When and Where to Trust the Teacher: Unifying On-Policy Distillation and GRPO through Entropy-Calibrated Credit Assignment

Reinforcement learning with verifiable rewards (RLVR) supervises mathematical reasoning through final-answer correctness, but provides little guidance on individual tokens. On-policy distillation (OPD) supplies dense feedback on student-generated responses, yet teacher preference need not reflect correctness. Recent hybrids combine OPD and verifier-derived advantages or reweight task credit using teacher ratios. However, teacher guidance enters after verifier-based group normalization, and token reweighting need not preserve the total task credit assigned to each response. We introduce Unified Entropy-Calibrated Credit Redistribution for GRPO (UECR-GRPO), which integrates verifier and teacher signals within a single GRPO-style update at both the response and token levels. \emph{Path-Utility Unification} (PUU) combines verifier reward and a teacher-to-anchor path log-ratio in a single KL-regularized objective. Its on-policy implementation uses a length-normalized teacher score and combines both rewards before group normalization and PPO clipping, allowing teacher evidence to influence the response ranking. \emph{Entropy-Calibrated Redistribution} (ECR) then uses the signed teacher--old-policy token gap to redistribute the verifier-derived component. Full-vocabulary teacher entropy attenuates uncertain guidance, while a response-wise zero-sum projection preserves the total task credit and its token-wise sign before clipping. Across five mathematical reasoning benchmarks, UECR-GRPO achieves average

\mathrm{Avg@12}

accuracies of 17.21% and 65.09% with Qwen3-1.7B and Qwen3-4B students, respectively, exceeding the strongest baseline at each scale by 0.89 and 0.56 percentage points.

Jie Zhang, Jingxiao Yang, Zhehao Huang +2

Shanghai Jiao Tong University · Zhejiang University

RL for Language Model Reasoning Group Relative Policy Optimization Credit Assignment in RL Reinforcement Learning with Verifiable Rewards On-Policy Distillation

Sep 23, 2026cs.LG

RL Starts before RL: On Policy Distillation for Better Reinforcement Learning

Reinforcement learning (RL) improves reasoning, but its performance depends on the policy from which training begins. We study on-policy distillation (OPD) as a preparation stage for RL and ask whether its benefits extend beyond improvements in the distilled model's initial accuracy. Under shared RL settings, students initialized with OPD reach higher final performance than those trained with direct RL or supervised fine-tuning followed by RL. This advantage can emerge even when OPD produces little immediate improvement in accuracy. Pre-RL Pass@k does not fully explain the benefit: similar or even higher values do not necessarily lead to better performance after RL. Behavioral analyses point to alignment with the teacher's distribution beyond top-1 agreement as a possible explanation. Such alignment may favor higher-quality reasoning paths while retaining alternatives that RL can further refine using outcome feedback. We further examine how trajectory sources and divergence objectives affect the value of distillation for subsequent RL. Standard reverse-KL OPD performs better before RL, but forward-KL OPD overtakes it afterward; with teacher-generated distillation trajectories, reverse KL remains ahead at both stages. These findings suggest that the preferred distillation objective depends on both the trajectory source and the training that follows. Our results support evaluating OPD as preparation for RL and selecting distillation choices by the performance achieved after subsequent training.

Shuai Dong, Yongfu Zhu, Yuqi Xu +26

Fudan University · SII · Peking University +2

Reinforcement Learning RL for Language Model Reasoning On-Policy Distillation RL Post-Training

Sep 23, 2026cs.LG

DCRL: Decoupling and Coupling Reinforcement Learning via Policy-Reward Manifold Alignment

Reinforcement learning (RL) has emerged as a key paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing reward systems, such as rule-based and reward-model-based, often exhibit issues such as unstable optimization and reward hacking. In this work, we revisit the general reasoning of LLMs from a geometric perspective, conceptualizing it as a coupled manifold composed of three interdependent sub-manifolds: logical deduction, evaluation, and representation. Based on this perspective, response generation in RL can be interpreted as a decoupling process from the evaluation manifold, while reward estimation corresponds to a decoupling process from the logical deduction manifold. The limitations of rule-based and reward-model RL systems can be geometrically interpreted as the mismatch of policy-reward manifolds during RL process. To address the aforementioned misalignment, we propose Decoupling and Coupling Reinforcement Learning (DCRL) framework, which incorporates two key components: (1) a syllogistic logic-based prompt evolution mechanism that dynamically refines reward rubrics to enhance the expressiveness of the reward manifold; and (2) a policy-reward re-coupling mechanism that jointly updates the reward and policy models, ensuring consistent evaluation and mitigating manifold mismatch during training. Theoretical analysis and extensive experiments across multiple reasoning domains demonstrate that DCRL consistently outperforms both rule-based and reward-model baselines. Notably, a Qwen3-4B model trained under DCRL surpasses a Qwen3-32B baseline and approaches the performance of a Qwen3-235B model, highlighting superior effectiveness and generalization in RL.

Henan Sun, Zehua Li, Haitao Hu +4

The Hong Kong University of Science and Technology (Guangzhou) · Huawei Noah’s Ark Lab · Tencent HY +1

Reinforcement Learning RL for Language Model Reasoning Rubric-Based RL Reward Design for RL

Sep 23, 2026cs.CL

Planned Test-Time Scaling with Coordinated Reasoning Paths

Test-time scaling with parallel branches is widely adopted to improve performance on challenging reasoning tasks. The predominant approach, repeated sampling, draws branches independently from a single policy, which can produce redundant attempts and thereby limit the gains from additional inference compute. To address this limitation, we propose Planned Test-Time Scaling (PTTS), which replaces independent sampling with a coordinated joint policy: a planner generates a solution outline for each branch, steering the branches toward distinct reasoning paths, and an executor produces a full solution conditioned on each outline. Formally, we show that PTTS strictly generalizes repeated sampling and, in a stylized setting, provably promotes coverage of complementary reasoning modes and yields better pass@k scaling. We instantiate PTTS on top of strong reasoning models, keeping them fixed as executors while replacing repeated sampling with PTTS inference to further enhance test-time scaling. Concretely, we develop two variants: PTTS-ZS prompts a model to jointly generate outlines for all branches in a single autoregressive pass, while PTTS-RL directly optimizes the planner against the pass@k reward using truncated execution rollouts for efficient training and a sharper reward signal. Across five mathematical reasoning benchmarks with Qwen3-1.7B and 4B, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL further increases the gain to up to 13.4 points. Further analysis indicates that broader coverage of distinct reasoning paths contributes to these gains. Overall, PTTS provides a general framework for improving test-time scaling by coordinating reasoning branches, with zero-shot and trainable instantiations that yield substantial performance gains.

Xueqing Wu, Langxing Bai, Hritik Bansal +5

University of California, Los Angeles · Amazon

RL for Language Model Reasoning Test-Time Scaling LLM Reasoning

Sep 22, 2026cs.CL

Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning

Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.

Yuqing Zhou, Hong Wang, Manqing Mao +8

George Mason University · Amazon, Inc

RL for Language Model Reasoning Step-Level Credit Assignment in RL Efficient Language Model Reasoning LLM Mathematical Reasoning

Sep 22, 2026cs.CL

Beyond Repeated Sampling: Learning Search Policies for LLM Reasoning

Large language models increasingly tackle hard reasoning problems by spending more test-time compute, yet the dominant strategy remains naive repeated sampling: draw many independent solutions and hope one is correct. Because such sampling explores only through local decoding noise, it tends to produce many near duplicate attempts rather than genuinely different ideas. We ask whether exploration can instead be steered at a semantic level, by first sampling problem specific concepts, hints, or strategies and then conditioning answer generation on them. We refine this into a simple, more exploratory procedure that emits many diverse concepts in a single trajectory, and evaluate it on hard problems where repeated sampling struggles. We then go a step further and make concept generation trainable: a small concept generator is optimized with reinforcement learning so that its concepts maximize the downstream success of a larger, frozen answer generator. On hard mathematical reasoning problems, the trained concept generator substantially improves the answer generator's pass@k over naive repeated sampling at the same answer generation allocation, surpasses concepts drawn from much larger untuned models, and transfers to answer generators it was never trained against, including a model from a different family. A small model can thus be trained into an effective, reusable search policy for a much larger one.

Ismail Labiad, Matthieu Kowalski, Marc Schoenauer +2

Meta FAIR · Université Paris-Saclay, LISN, Inria, CNRS · NYU Courant Institute and CDS

RL for Language Model Reasoning LLM Reasoning

Sep 22, 2026cs.LG

PACT: From Credit Assignment to Critic Alignment

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

Jiayan Fu, Hang Xu, Yong Zhang +4

AllSpark Team

Reinforcement Learning Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL RL Post-Training Actor-Critic Methods+1

Sep 21, 2026cs.AI

Rollout Efficiency in Reinforcement Learning for Reasoning Large Language Models: A Taxonomy and Future Directions

Reasoning-oriented reinforcement learning enables large language models to solve mathematical, coding, and other multi-step tasks, but shifts a substantial portion of the training cost to rollout, where trajectories are generated for policy updates. Efficient rollout mechanisms are therefore essential to reduce this cost while maintaining the freshness, consistency, and statistical validity of training data. This survey provides a systematic taxonomy of recent research on rollout efficiency for reasoning-oriented reinforcement learning, classifying existing approaches from both mechanism and bottleneck perspectives. Based on this taxonomy, we analyze how different technique families address distinct sources of rollout inefficiency, examine opportunities and potential conflicts for combining them, identify gaps in the evaluation and reporting of efficiency gains, and discuss open challenges and future research directions.

Niloofar Gholipour, Marcos Assuncao, Gursimran Singh +8

École de technologie supérieure, Univ. of Québec, Canada · Huawei Technologies, Canada · The Univ. of Melbourne, Australia +1

LLM Inference Efficiency Reinforcement Learning RL for Language Model Reasoning Efficient Language Model Reasoning

Sep 21, 2026cs.CL

TelecomGPT-R1: Unified Post-Training for Reasoning Across Heterogeneous Telecom Tasks

Large language models (LLMs) offer great potential to automate a broad range of telecom engineering tasks by reasoning over standards, network configurations, mathematical models, source code, and operational logs. However, existing telecom LLMs struggle to reliably reason across these diverse tasks and data types. General-purpose LLMs often lack reliable grounding in telecom-specific knowledge, while telecom-specialized models are typically developed for narrower task families and exhibit limited multi-task performance. To fill this gap, we introduce TelecomGPT-R1, a family of open source unified telecom reasoning models structured around four complementary axes: protocol, knowledge, modeling, and fault. We first develop an axis-aware data generation framework that refines coarse public telecom artifacts into verified question-answer pairs and high quality chain-of-thought (CoT) reasoning trajectories, yielding a training corpus containing 104,880 examples. Building on this corpus, supervised fine-tuning (SFT) instills telecom knowledge and evidence-grounded reasoning patterns to overcome the cold start barrier for reinforcement learning (RL). We then apply dynamic sampling policy optimization (DAPO) with task-routed rubric rewards to keep RL updates informative and stable across heterogeneous telecom reasoning tasks. These rewards decompose axis-specific CoT traces into verifiable reasoning units and combine grounded dense process credit with outcome correctness, allowing RL to learn generalizable problem solving behaviors from verifiable telecom evidence. We release the TelecomGPT-R1 models and a reproducible training recipe to support further community development. Evaluations on seven benchmarks of the GSMA Open Telco Leaderboard show that the open-source TelecomGPT-R1-27B achieves an 89.64% mean score, outperforming leading proprietary models, including GPT-5, Claude, and Gemini.

Bohao Wang, Chenwei Wu, Hang Zou +7

College of Information Science and Electronic Engineering, Zhejiang University, 310027 Hangzhou, China · Research Institute for Digital Future, Khalifa University, P O Box 127788, Abu Dhabi, UAE · Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122, USA +1

LLM Grounding RL for Language Model Reasoning LLM Post-Training

Sep 21, 2026cs.AI

Fathom-Vaidya: Advancing Medical Reasoning with Rubric-Based Rewards

Deploying Large Language Models (LLMs) in healthcare requires robust performance across two complementary dimensions - diagnostic reasoning: the convergent, evidence-driven task of inferring a patient's condition from clinical data to produce a diagnosis, and clinical healthcare reasoning: the broader, navigational judgment required to communicate, plan, and adapt across multi-turn clinical interactions where a single correct answer may not exist. Recent benchmarks such as HealthBench and MedXpertQA reveal persistent weaknesses in both areas, exposing failures in complex diagnostic scenarios and limitations in contextual, patient-centered dialogue. We introduce a sequential training framework that targets these facets using synthetic data and rubric-based reinforcement learning. First, we improve diagnostic reasoning using MedBullets-derived questions with rule- and rubric-guided Reinforcement Learning (RL). We then shift to clinical reasoning by generating 5.3k synthetic multi-turn scenarios, each paired with multi-dimensional rubrics to comprehensively assess the response. This approach yields over 10% improvement on MedXpertQA, and our 30B model achieves 50.1% accuracy on HealthBench-Hard, surpassing proprietary baselines including GPT-5 (thinking). Our results show that targeted synthetic datasets and rubric-based training can systematically improve both diagnostic and interactive clinical reasoning in medical LLMs.

Kalash Shah, Kunal Singh, Snehan J +1

Fractal AI Research

RL for Language Model Reasoning Rubric-Based RL Clinical Reasoning Medical Reasoning Medical LLMs