Reinforcement Learning with Verifiable Rewards

Also known as RLVR

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59 papers in the last four weeks, up 119% on the four weeks before. 0.6% of all new papers.

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Jun 3, 2026cs.LG

TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition

Large language models (LLMs) have made remarkable progress in reasoning tasks, largely driven by post-training paradigms, especially reinforcement learning with verifiable rewards (RLVR). However, a critical bottleneck persists: RLVR fails on highly challenging zero-reward problems, where all sampled reasoning trajectories yield uniformly failed outcomes, providing no optimization signal to drive model improvement. Prior efforts to address this limitation, such as dense process supervision, partial reward assignment, or prefix-guided exploration, suffer from inherent task constraints or do not fully equip the policy model with the capabilities necessary to solve the original intractable problems. To address this, we propose TD-Grokking, a training-time decomposition framework for zero-reward problems. It recursively decomposes intractable root problems into self-contained, verifiable subproblems, forming hierarchical trees where solvable leaves provide non-zero rewards. Evaluations on mathematical and medical tasks show that TD-Grokking outperforms vanilla GRPO as well as all baseline approaches. Together with detailed analysis, these results confirm that training-time decomposition effectively converts zero-reward examples into usable training signals, enabling consistent performance gains. Our code and datasets are available at https://anonymous.4open.science/r/TD-Grokking-6567/.

Ningyuan Xi, Hao Xu, Hongsheng Xin +1

Department of Data Science, City University of Hong Kong. · Hong Kong Institute of AI for Science, City University of Hong Kong. · Li Auto Inc.

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

Jun 3, 2026cs.LG

Smart Picks in the Dark: Towards Efficient RLVR for Reasoning via Tracing Metacognitive Pivots

Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset. To this end, data-efficient RLVR methods have been widely studied from two perspectives: (i) data selection methods identify a small subset of "golden" samples that yield near-full-data performance, but they rely on a pre-existing pool of labeled data. (ii) unsupervised RLVR methods train the model using its own internal supervision signals on large-scale unlabeled data, yet they exhibit suboptimal performance. Accordingly, we investigate the "pick in the dark" setup for RLVR, which aims to select, without prior supervision, unlabeled samples that are most beneficial for training and worthy of annotation. Through systematic analysis, we demonstrate that smart picks hinge on a well-calibrated uncertainty estimator to enable strategic partitioning of data for adaptive training regimes. Building on this insight, we propose PivotTrace, a three-way data triage framework that leverages attention dynamics to trace metacognitive pivots during reasoning. By precisely quantifying uncertainty through pivot density, PivotTrace achieves automated data routing to synergistically maximize both annotation and training efficiency. Empirically, PivotTrace surpasses the fully supervised LRM with only 29.3% annotated samples and 2.75 faster convergence.

Guangcheng Zhu, Shenzhi Yang, Haobo Wang +7

1Zhejiang University · 2Ant Group

Uncertainty Quantification RL for Language Model Reasoning Active Learning Reinforcement Learning with Verifiable Rewards Data-Efficient Learning

Jun 2, 2026cs.AI

Entropy Is Not Enough: Unlocking Effective Reinforcement Learning for Visual Reasoning via Vision-Anchored Token Selection

While token-level entropy is commonly recognized as effective for credit assignment in text-only reinforcement learning with verifiable rewards (RLVR), it remains unclear whether this mechanism still holds in visual reasoning. Our controlled study shows that this mechanism collapses in visual reasoning due to the omission of vision-sensitive tokens with naturally low entropy. Although existing multimodal RL methods increasingly acknowledge the importance of visual perception, they struggle to satisfy the inherent demand for interleaving precise perceptual grounding with semantic reasoning, either lacking systematic visual measurements or overlooking that token entropy primarily drives semantic exploration. To address this, we introduce VEPO (Vision-Entropy token-selection for Policy Optimization), an effective RL framework explicitly integrating visual sensitivity with token entropy via a principled multiplicative coupling, where VEPO redirects gradient credit toward tokens which are simultaneously visually grounded and highly informative. Extensive experiments demonstrate VEPO's leading performance, significantly outperforming the entropy-only baseline by 2.28 points at 7B-scale and 3.15 points at 3B-scale. Ablations further substantiate the soundness of our method.

Senjie Jin, Peixin Wang, Boyang Liu +8

College of Computer Science and Artificial Intelligence, Fudan University

Token-Level Credit Assignment Visual Reasoning VLM Reasoning Reinforcement Learning with Verifiable Rewards Visually Grounded Reasoning RL for VLMs

Jun 2, 2026cs.CL

Synthesize and Reward -- Reinforcement Learning for Multi-Step Tool Use in Live Environments

Training LLMs to orchestrate multi-step tool calls is held back by three coupled obstacles: realistic stateful execution environments are costly to build, synthetic training queries are often detached from the server's actual state (so the generated tool calls fail to execute), and recall-based RL rewards incentivize verbose tool-calling patterns. We present PROVE (Programmatic Rewards On Verified Environments), a framework with three contributions: (1) a library of 20 stateful MCP (Model Context Protocol) servers exposing 343 tools, enabling live-execution RL training with session-scoped state isolation; (2) a state-machine data synthesis pipeline that generates multi-turn tool-call trajectories grounded in live-sampled server state, so generated queries reference entities that actually exist; and (3) a multi-component programmatic reward with an adaptive efficiency penalty that counters the verbosity incentive of recall-based rewards. We train four models (Qwen3-4B, Qwen3-8B, Qwen2.5-7B, Granite-4.1-8B) with GRPO on the resulting ~13K training examples. On BFCL Multi-Turn, tau2-bench, and T-Eval, PROVE yields improvements of up to +10.2, +6.8, and +6.5 points respectively, demonstrating that this framework yields consistent gains on multi-step tool orchestration across two model families.

Ibrahim Abdelaziz, Asim Munawar, Kinjal Basu +4

IBM Research

Synthetic Data Generation Reinforcement Learning with Verifiable Rewards LLM Agent Training Tool Use RL for Tool Use

Jun 2, 2026cs.LG

Trading Human Curation for Synthetic Augmentation in RLVR

The supply of high-quality training tasks is a central bottleneck for reinforcement learning from verifiable rewards (RLVR) on agentic language models. Each task requires a sandboxed setup, a prompt, and a hand-authored reward function, and only tasks that pass a quality bar produce useful training signal. Hand-curation at this quality bar does not scale economically to the task counts effective RL training requires, and the substitution rate between automatically generated task variants and human-authored ones is not yet established. We investigate using pre-specified, gate-filtered augmentations of a small hand-authored base as a substitute for additional human curation during RLVR. We formalize the cost-adjusted trade rate

ρ_{\text{cost}}

between augmented and human-authored tasks, measure it through a controlled ablation across training corpora with varying augmentation share, and characterize the end-to-end economics of the augmentation pipeline. Substituting augmented content for additional human-authored tasks retains aggregate held-out generalization on a ten-benchmark suite spanning code, instruction following, reasoning, and multi-turn agentic function-calling. The cost-adjusted trade rate

ρ_{\text{cost}}

between gated synthetic and human-authored RLVR tasks stays in

[1.4\times, 11.6\times]

across the plausible

c_{\text{human}}/c_{\text{aug}}

range.

Akshansh, Leonardo Rosa Rodrigues, Michael Korostelev +2

Pareto AI

Synthetic Data Augmentation Reinforcement Learning with Verifiable Rewards RL for LLM Agents

Jun 2, 2026cs.LG

Exploiting Verification-Generation Gap: Test-Time Reinforcement Learning with Confidence-Conditioned Verification

Test-time reinforcement learning has emerged as a promising paradigm for enhancing the complex reasoning abilities of large language models in a completely label-free manner. Despite existing studies focusing on Pass@1 performance, optimizing Pass@k remains under-explored yet critical in label-free settings, which measures generation coverage for sustained exploration. Optimizing Pass@k in label-free setting is highly non-trivial, as directly applying the Pass@k advantage designs effective for RLVR yields unsatisfactory performance. Through in-depth empirical analysis, we discover the root causes hindering performance: pseudo-label estimations for low-confidence samples have a high probability of being incorrect, while candidate answers for high-confidence samples suffer from severe diversity collapse. To overcome these hurdles, we propose TTRL-CoCoV (Test-Time Reinforcement Learning with Confidence-Conditioned Verification), a novel confidence-adaptive framework that expands Pass@k coverage and improves Pass@1 performance. Based on our key insight that verification capability generally leads generation capability, TTRL-CoCoV employs a confidence-conditioned mechanism: for high-confidence samples, it bootstraps verifier and applies an exploration-enhancing reward to prevent diversity collapse; for low-confidence samples, it delegates pseudo-label selection to the verifier to filter incorrect pseudo-labels; and for medium-confidence samples, it bypasses verification entirely. Extensive experiments demonstrate that TTRL-CoCoV outperforms the best competing methods across 6 widely-recognized benchmarks, achieves average absolute gains of +9.8% in Pass@1 and +18.7% in Pass@16 over TTRL, and even achieves absolute Pass@1 improvements of up to +5.0% across multiple reasoning benchmarks when compared against fully supervised RL methods. Our code repository: https://github.com/shanjf666/CoCoV.

Jiahui Li, Jianfeng Shan, Wenpei Chen +5

1Sun Yat-Sen University · University of Science and Technology of China · 3National University of Singapore

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

Jun 2, 2026cs.LG

Right Makes Might: Aligning Verified Hidden States Empowers RL Reasoning

Reinforcement Learning from Verifiable Rewards (RLVR) has become the dominant approach for improving mathematical reasoning in large language models, yet current methods reduce each correct rollout to a single reward bit, ignoring the geometric structure shared among their hidden states. Investigating this structure, we find that at the anchor token (the position immediately before the answer marker), correct rollouts converge naturally because they must produce the same answer (cosine similarity ~0.84), yet each retains residual variance from its unique reasoning path. Encouraging full alignment at this point pushes the model to extract a unified "correct decision" representation, reducing sensitivity to which reasoning path was taken. Based on this observation, we propose Hidden-Align, an auxiliary loss function that aligns the last-layer hidden states of correct rollouts at the anchor token during RL training, with zero overhead in both training and inference. On eight mathematical reasoning benchmarks, Hidden-Align improves average pass@1 over the DAPO baseline by 3.8, 6.2, and 5.4 percentage points on Qwen3-1.7B, 4B, and 14B respectively, with consistent pass@k gains across all three scales, supported by ablations on loss type, anchor position, layer depth, and loss weight.

Ziyue Wang, Aomufei Yuan, Yongfu Zhu +10

1Peking University · 2JINGDONG · 3Shanghai Innovation Institute +2

LLM Alignment RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards LLM Mathematical Reasoning

Jun 2, 2026cs.LG

Learning to Solve, Forgetting to Retain: Correct-Set Turnover in RLVR

Reinforcement learning with verifiable rewards (RLVR) improves the ability of large language model, yet headline accuracy gains often conceal a hidden cost: previously solved problems quietly become unsolvable as training proceeds. We frame this phenomenon as \emph{correct-set turnover}, representing the coupled dynamics of solution acquisition and regression over the mastered set. Under this view, retention becomes an explicit optimization target alongside acquisition. We analytically and empirically establish the \emph{repair-window principle}: the cost of restoring a regressed prompt grows sharply with review delay, defining a low-cost window that standard RLVR pipelines fail to exploit. To address this, we propose \textbf{\method{}}, a retention-aware review mechanism that tracks mastered prompts and periodically reintroduces them to \textbf{remind} the model of previous solutions. By utilizing pre-rollout batch replacement, \method{} incurs zero additional rollout overhead. Evaluated across 20 benchmarks spanning image-text, video, and text-only tasks with Qwen3-VL and Qwen2.5-Math, \method{} consistently improves performance over GRPO, DAPO, and replay baselines, demonstrating robust generalizability across modalities and algorithms.

Chuanyu Qin, Chenxu Yang, Qingyi Si +3

Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

Continual Learning for LLMs Reinforcement Learning Replay-Based Continual Learning Reinforcement Learning with Verifiable Rewards RL Post-Training

Jun 2, 2026cs.LG

Self-Distilled Policy Gradient

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

Yifeng Liu, Shiyuan Zhang, Yifan Zhang +1

Department of Computer Science, University of California, Los Angeles, CA, USA · Princeton AI Laboratory, Princeton University, Princeton, NJ, USA

Policy Gradient On-Policy Self-Distillation Reinforcement Learning with Verifiable Rewards Policy Gradient Methods

Jun 2, 2026cs.CL

Hint-Guided Diversified Policy Optimization for LLM Reasoning

Recent developments in Large Language Models (LLMs) have showcased impressive reasoning capabilities, with Reinforcement Learning with Verifiable Rewards (RLVR) being a promising enhancement strategy. However, existing reward mechanisms are constrained to the outcome-level correctness and lack explicit signals to guide the model to consider diverse solutions. In contrast, human problem solving typically involves evaluating multiple potential approaches and selecting the most reliable solution, a cognitive process that current RLVR frameworks do not explicitly incentivize. Inspired by this, we propose Hint-Guided Diversified Policy Optimization (HDPO), allowing the model to first list all potential candidate solution outlines as hints and then select the most reliable one for further reasoning. HDPO comprises two stages of Cold Start for Structured Reasoning and Hint-Guided Diversified Reinforcement Learning to incentivize the model to generate diverse and reliable solutions following the ``propose-select-think'' trajectory. Experimental results show that HDPO effectively boosts LLM reasoning and enhances the diversity of candidate solutions as well as the LLM's ability to identify reliable solutions.

Zhiyu Cao, Kaixin Wu, Mingjie Zhong +4

School of Computer Science and Technology, Soochow University, Suzhou, China · Ant Group, Hangzhou, China

Reasoning Diversity RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards LLM Reasoning

Jun 1, 2026cs.AI

CAPF: Guiding Search-Agent Rollouts with Credit-Attenuated Privileged Feedback

Recent LLM search agents use reinforcement learning with verifiable rewards (RLVR) to learn search-augmented reasoning from outcome rewards. On hard problems, these agents rarely sample end-to-end successful rollouts, leaving outcome-only RLVR with few positive-reward trajectories. We argue that improving learning on such problems requires additional guidance during training, and RLVR already contains verifier-side information that can provide it. This information can identify errors or omissions in the agent's submitted answer and guide revision within the rollout. We propose a training-time mechanism called \textbf{Credit-Attenuated Privileged Feedback} (CAPF), which makes this verifier-side information available through a Privileged Feedback call during training. CAPF lets the policy revise zero-reward attempts into positive-reward repair trajectories and attenuates credit for the feedback call and earlier actions to accommodate deployment without this call. Empirical research demonstrates that CAPF improves Qwen3-4B's average exact-match score from 44.7% under outcome-only RLVR to 48.5% on seven open-domain QA benchmarks.

Bin Chen, Xinye Liao, Yiming Liu +2

RL for Language Model Reasoning Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Learning Using Privileged Information Open-Domain QA

Jun 1, 2026cs.AI

TRON: Targeted Rule-Verifiable Online Environments for Visual Reasoning RL

Reinforcement learning (RL) for visual reasoning needs scalable, verifiable, and controllable training signals. Existing visual RL post-training trains on static curated datasets, with fixed image-question-answer samples bounded by their collection budget. In this work, we introduce TRON (Targeted, Rule-verifiable Online eNvironments), an online environment substrate: a training rollout is generated on demand by a controllable generator-verifier program that samples a fresh latent visual state, renders an image, asks a question, and exactly verifies the answer. A single run can therefore draw an unbounded stream of fresh instances at the difficulty level required by the current curriculum. The current TRON suite contains 520 environments organized into five ability buckets (spatial, mathematical, diagram, pattern/logic, and counting); the same substrate supports both a single full model trained on all buckets and per-bucket ability-specialist models, with no additional data collection. We also introduce a substrate analysis covering generation reliability, instance and level diversity, cross-environment near-duplicates, and base-model pass rate by difficulty level. RL post-training with METHOD consistently improves performance on ten external multimodal reasoning benchmarks across Qwen3-VL-4B, Qwen2.5-VL-7B, and MiMo-VL-7B-SFT.

Tianze Yang, Yucheng Shi, Ruitong Sun +3

University of Georgia

Reinforcement Learning VLM Reasoning Reinforcement Learning with Verifiable Rewards Visually Grounded Reasoning RL Post-Training Visual RL

May 31, 2026cs.LG

RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoning

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.

Yixiu Mao, Yun Qu, Qi Wang +2

Department of Automation, Tsinghua University

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

May 31, 2026cs.CL

Deep Research as Rubric for Reinforcement Learning

Open-ended reasoning and long-form generation tasks lack reliable automatic verification signals for reward-based policy optimization. Rubrics offer a promising alternative, but existing approaches treat them as given artifacts -- either hand-crafted or prompt-generated -- and often miss the task-specific, knowledge-intensive dimensions that matter most, distorting the reward signal. Our key observation is that rubric construction is itself a research problem: identifying what makes a response correct or insightful requires discovering and synthesizing external knowledge. We propose Deep Research as Rubric (DR-rubric), a two-stage framework for constructing such rubrics. Stage I elicits domain facts, structural constraints, and failure modes through iterative multi-turn agentic search; Stage II distills this evidence into atomic, independently verifiable constraints for GRPO-based policy optimization. Because the model under training can serve as its own rubric generator, DR-rubric-8B supports bootstrap rubric generation without frontier-model assistance. We evaluate on 6 benchmarks spanning agentic research and expert reasoning. Experiments show that DR-Rubric achieves strong competitive performance with only 1K -- 3K training instances, where GPT-5-generated rubrics particularly benefit breadth coverage on agentic tasks, Gemini-generated rubrics yield the most balanced performance across agentic and expert reasoning tasks, and bootstrap rubrics exhibit a specialization-to-rebalancing evolution achieving the best overall performance at the third iteration. Results demonstrate that reframing rubric construction from static evaluation templates into an evidence-driven research process yields more scalable, fine-grained reward signals for open-ended tasks.

Wangyi Mei, Zhouhong Gu, Zhenhan Bai +9

Fudan University · Xiaohongshu Inc. · Beijing University of Posts and Telecommunications

Open-Ended Generation Reinforcement Learning RL for Language Model Reasoning Rubric-Based RL Reinforcement Learning with Verifiable Rewards Rubric-Guided Generation+1

May 31, 2026cs.AI

Before the Model Learns the Bug:Fuzzing RLVR Verifiers

Reinforcement learning with verifiable rewards (RLVR) replaces human preference labels with executable reward functions such as math answer checkers, JSON tool-call validators, and code unit-test harnesses. That makes the reward partly a software artifact: if the verifier is wrong, optimization can learn the bug. We study this failure mode with a lightweight verifier-fuzzing framework that generates adversarial completions, compares buggy and stricter reference verifiers, logs paired decisions, and reports false-positive, false-negative, disagreement, exploit, and uncertainty metrics.

Jaideep Ray

Reward Hacking Automated Software Testing Reinforcement Learning with Verifiable Rewards

May 29, 2026cs.CL

LongTraceRL: Learning Long-Context Reasoning from Search Agent Trajectories with Rubric Rewards

Long-context reasoning remains a central challenge for large language models, which often fail to locate and integrate key information in extensive distracting content. Reinforcement learning with verifiable rewards (RLVR) has shown promise for this task, yet existing methods are limited by low-confusability distractors and sparse, outcome-only reward signals that cannot supervise intermediate reasoning steps. To address these issues, we introduce \textsc{LongTraceRL}. For data construction, we generate multi-hop questions via knowledge graph random walks and leverage search agent trajectories to build \emph{tiered distractors}: documents the agent read but did not cite (high confusability) and documents that appeared in search results but were never opened (low confusability), producing training contexts that are far more challenging than those built by random sampling or one-shot search. For reward design, we propose a \emph{rubric reward} that uses the gold entities along each reasoning chain as fine-grained, entity-level process supervision. This rubric reward is applied only to responses with correct final answers (positive-only strategy), distinguishing the reasoning quality among correct responses and preventing reward hacking. Experiments on three reasoning LLMs (4B--30B) across five long-context benchmarks demonstrate that \textsc{LongTraceRL} consistently outperforms strong baselines and encourages comprehensive, evidence-grounded reasoning. Codes, datasets and models are available at https://github.com/THU-KEG/LongTraceRL.

Nianyi Lin, Jiajie Zhang, Lei Hou +1

Tsinghua University

LLM Grounding RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Process Supervision Long-Context Inference

May 29, 2026cs.AI

CAST: Non-Privileged Clipped Asymmetric Self-Teaching with Advantage Flipping for GRPO

Reinforcement learning with verifiable rewards (RLVR), especially Group Relative Policy Optimization (GRPO), has been widely used to improve reasoning in large language models. However, outcome-level rewards provide only sparse supervision, and group-relative advantages vanish when all sampled trajectories for a prompt are either correct or incorrect. On-Policy Self-Distillation (OPSD) offers dense token-level guidance, but its token preferences are not necessarily aligned with trajectory correctness; empirical diagnostics show that OPSD signals behave differently on correct and incorrect rollouts, with teacher-positive and teacher-negative gap signals exhibiting different noise profiles. These diagnostics are conducted under an OPSD-style privileged teacher context for analysis only, whereas CAST training uses answer-free self-teacher scoring.Motivated by these observations, this work proposes CAST, an answer-free self-distillation method for GRPO-style RLVR. CAST keeps the verifier-grounded GRPO objective, but uses a stop-gradient self-teacher to shape token-level advantages according to trajectory correctness. Unlike prior self-distilled RLVR methods, CAST does not require reference-solution-conditioned teacher scoring, keeps the self-teacher log-probability gap active throughout training, and applies bidirectional local advantage sign reversal: teacher-negative tokens in correct trajectories can receive negative token-level advantages, while teacher-positive tokens in incorrect trajectories can receive bounded positive local advantages. For zero-variance all-correct and all-wrong groups, CAST assigns bounded sign-constrained base advantages, so these otherwise zero-gradient groups can contribute verifier-signed token feedback. Experiments on mathematical reasoning show that CAST improves RLVR training while retaining a lightweight, verifier-grounded trajectory-level objective.

Yang Li, Gongle Xue, Yijia Guo +3

School of Software and Microelectronics, Peking University, Beijing · School of Artificial Intelligence, Peking University, Beijing · School of Computer Science, Peking University, Beijing +1

RL for Language Model Reasoning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards On-Policy Distillation Teacher-Student Learning

May 29, 2026cs.LG

EchoRL: Reinforcement Learning via Rollout Echoing

Reinforcement Learning with Verifiable Rewards is an effective route for post-training to strengthen the reasoning capability of large language models. However, as training proceeds, the learning signal can collapse thus makes the training gain become marginal and ineffective. Specifically, a growing fraction of prompts' rollouts become advantage-degenerated: all the self-generated rollouts show verified-success, making the standard deviation over their rewards be zero; accordingly each rollout's advantage becomes degenerated (zero) as well. Given such rollouts' advantages, the policy-gradient for model optimization eventually vanishes, capping the training performance. We argue that some of these rollouts still contain valuable learning signals but unfortunately omitted with the existing RLVR methods. In this paper, inspired through analyzing the entropy pattern behind golden trajectories produced by external expert models, we propose EchoRL for better exploiting the advantage-degenerated rollouts to further improve the training performance. EchoRL is a lightweight module that first identifies an EchoClip from verified-success rollouts based on their step-level entropy values, and then feeds this clip back as an auxiliary supervision signal in the RL objective. Extensive experiments across 10 benchmarks, 5 LLM backbones, and 4 popular RLVR post-training methods demonstrate that EchoRL consistently improves RLVR post-training with minimal overhead.

Jinhe Bi, Aniri, Minglai Yang +9

Huawei Heisenberg Research Center · LMU Munich · Munich Center for Machine Learning +5

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

May 29, 2026cs.CL

Combinatorial Synthesis: Scaling Code RLVR via Atomic Decomposition and Recombination

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as the cornerstone for shaping the remarkable coding abilities of Large Language Models (LLMs). However, the scalability of RLVR is severely constrained by the scarcity of sufficiently challenging verifiable code tasks that target near the model's edge of competence. Prior studies often rely on heuristic seed expansions for data synthesis, which severely limits both novelty and difficulty. Consequently, the training value of such data fails to scale proportionally with the size of its synthesis. To this end, we propose Atomic Decomposition and Recombination (ADR), a novel framework that generates verifiable code tasks via decomposition into atomic elements and controlled recombination, thereby enabling the generation of genuinely novel and challenging verifiable code tasks. Experiments and analysis demonstrate that ADR achieves superior originality, difficulty, diversity, and test quality over existing baselines, and consistently delivers greater improvements in code ability across RLVR in diverse downstream domains, including algorithmic programming, tool usage, and data science. Our work sheds light on a new paradigm for novel code task synthesis and scalable RLVR training.

Jiasheng Zheng, Boxi Cao, Boxi Yu +6

Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences · Lero the Research Ireland Centre for Software, University of Limerick · The Chinese University of Hong Kong, Shenzhen +1

RL for Code Generation Reinforcement Learning with Verifiable Rewards Synthetic Data Generation for Language Models

May 29, 2026cs.LG

Automating Formal Verification with Reinforcement Learning and Recursive Inference

Automated formal verification remains challenging for large language models because data for proof assistants and verification-aware languages is scarce, and correctness depends on satisfying precise machine-checkable specifications rather than producing plausible code. This thesis studies how verifier environments can improve LLM generation of verified programs and proofs through reinforcement learning from verifiable rewards (RLVR) and verifier-guided inference-time search. First, we train open-source models in Dafny with RLVR using Group Relative Policy Optimization (GRPO) and related variants, assembling generated candidates into complete programs and scoring them with compiler and verifier outcomes. Initial experiments on an APPS-derived Dafny dataset increased verified reward from 2.2% to 58.1%, but revealed specification hacking, where models exploit weak formal specifications instead of implementing the intended solutions. After filtering underspecified and vulnerable tasks, multi-turn RLVR on the refined benchmark improves the verified pass rate from 9.7% to 31.1%. Second, we develop a verifier-guided inference scaffold in Lean that treats proof generation as structured search over decomposed subgoals, verifier feedback, diagnostics, and repair. With a fixed base model, the full scaffold with proof reviser improves pass rate on an initial VeriCoding pilot set from 46.2% under direct repair to 69.2%. On the larger VERINA dataset, whole-task decomposition plus proof reviser solves 7 of 42 previously unsolved tasks. We also introduce Dalek-Bench, a repository-scale Lean benchmark derived from the Rust

\texttt{curve25519-dalek}

verification project; preliminary results remain weak, indicating that stronger progress evaluation and task-specific tool-use policies are still needed.

Max Tan

Department of Electrical Engineering and Computer Science · Massachusetts Institute of Technology

RL for Code Generation Inference-Time Search Automated Theorem Proving LLM-Based Program Synthesis Formal Verification Reinforcement Learning with Verifiable Rewards

May 29, 2026cs.CV

Attend to Evidence: Evidence-Anchored Spatial Attention Supervision for Multimodal RLVR

Reinforcement learning with verifiable rewards (RLVR) improves vision-language models (VLMs) by optimizing outcome rewards derived from final answers. However, such outcome-only rewards do not tell the model which image regions justify an answer. For questions that require visual grounding, these rewards cannot distinguish responses supported by relevant visual evidence from those produced by language-prior shortcuts or lucky guesses. We introduce EASE (Evidence-Anchored Spatial Attention), which augments multimodal RLVR with visual-evidence process supervision. EASE converts annotated evidence regions into a smoothed visual-token target and uses it to guide response-to-image attention during RL training, but only on high-reward trajectories. The annotations are used solely as privileged training labels, while inference requires only the original image and question. Across Qwen2.5-VL-7B, Qwen3-VL-4B, and Qwen3-VL-8B, EASE raises average scores over DAPO by 2.5 to 3.1 points on perception, hallucination, visual math, and multimodal reasoning benchmarks. Diagnostics and ablations show that EASE better aligns visual attention with annotated evidence regions.

Ruina Hu, Chen Wang, Lai Wei +5

1Harbin Institute of Technology · 2Zhongguancun Academy · 4Nankai University +4

Reinforcement Learning with Verifiable Rewards Visually Grounded Reasoning Attention Mechanisms Visual Grounding Vision-Language Alignment RL for VLMs

May 28, 2026cs.SE

Improving Small Language Models for Code Generation with Reinforcement Learning from Verification Feedback

Reinforcement learning with verifiable rewards (RLVR) trains language models using programmatically checkable signals such as unit-test outcomes, enabling direct optimization for functional correctness in code generation. We conduct an empirical study of RLVR for Python code generation on the MBPP benchmark using two small models (Qwen3-0.6B and Llama3.2-1B) with LoRA fine-tuning. Across multiple reward formulations such as: unit-test-only rewards, static-analysis-only shaping via the Ruff linter, and a combined reward, we compare group-based policy optimization variants (GRPO and GSPO) and evaluate both functional correctness and behavioral diagnostics. In our experimental setting, RLVR improves pass@1 on MBPP test by up to 13 percentage points under proposed combined reward configuration. However, we find that reward shaping can induce systematic behavioral shifts: using only static-analysis penalties may bias the policy toward shorter completions that reduce lint errors without reliably improving functional correctness. In contrast, combined rewards mitigate this degeneration and yield more stable trade-offs between correctness and style constraints. Overall, our results highlight that RLVR effectiveness for code generation is highly sensitive to reward design and optimization granularity, and that diagnostics beyond pass@1, including generation length, Ruff severity profiles, and execution error types are useful for identifying failure modes.

Egor Skopin, Evgeny Kotelnikov

RL for Code Generation Reward Shaping Reinforcement Learning with Verifiable Rewards Code Generation Evaluation

May 28, 2026cs.LG

VeriGate: Verifier-Gated Step-Level Supervision for GRPO

Group Relative Policy Optimization (GRPO) is an effective recipe for training reasoning models with verifier-based outcome rewards, but its supervision is sparse: when all sampled trajectories for a prompt receive the same verifier reward, the group-relative advantage collapses to zero and learning stalls. Outcome-only rewards also provide no step-level credit assignment, limiting exploration and making it harder to learn robust reasoning. We present VeriGate (Verifier-Gated Step-Level GRPO), a verifier-gated extension of GRPO that addresses these limitations with three design choices. First, VeriGate keeps the verifier in charge whenever verifier rewards induce a meaningful preference among sampled trajectories, and uses process supervision only when verifier rewards are degenerate. Second, instead of collapsing Process Reward Model (PRM) step scores into a single trajectory reward, VeriGate converts them into future-cumulated rewards to assign continuation-aware credit. Third, VeriGate transforms these rewards into group-normalized token-level advantages, restoring informative gradients and fine-grained credit assignment while remaining less susceptible to reward hacking than methods that optimize aggregated PRM scores. Empirically, training on MATH with 1.5B and 7B Qwen2.5-Instruct models and evaluating on six reasoning benchmarks, VeriGate improves average accuracy by about 20% and 12% for 1.5B and 7B models respectively, substantially reduces zero-gradient failures, decreases reward-hacking behavior, and improves reasoning quality relative to outcome-only GRPO and PRM-as-outcome baselines.

Aakriti Agrawal, Minghui Liu, Furong Huang

University of Maryland, College Park

Process Reward Models RL for Language Model Reasoning Group Relative Policy Optimization Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Step-Level Credit Assignment

May 28, 2026cs.CV

Reinforcement Learning with Robust Rubric Rewards

While Reinforcement Learning with Verifiable Rewards (RLVR) is effective for deterministically checkable tasks, many vision-language tasks are partially verifiable, demanding multi-criteria supervision (e.g., perceptual details, reasoning steps, and constraints). Rubrics provide a natural interface for this fine-grained supervision, but their effectiveness depends on the execution accuracy during online RL. We propose Reinforcement Learning with Robust Rubric Rewards (

\text{RLR}^3

), extending RLVR from task-level verification to criterion-level verification.

\text{RLR}^3

routes instance-specific rubrics through two execution paths: an LLM-as-an-extractor paired with a deterministic verifier, or an LLM-as-a-Judge for non-verifiable criteria. To ensure faithful scoring,

\text{RLR}^3

introduce a minimal exposure strategy that masks ground truths from extractors and images from judges. Furthermore,

\text{RLR}^3

employs hierarchical aggregation to prioritize essential criteria over additional criteria, and mitigates score saturation within rollout groups. Evaluated on Qwen3-VL-30B-A3B across 15 benchmarks,

\text{RLR}^3

consistently outperforms RLVR, yielding a 4.7-point improvement over the base model and exceeding the official instruct-to-thinking model gap. Controlled audits confirm our deterministic verification and minimal exposure significantly reduce exploitable false positives.

Ya-Qi Yu, Hao Wang, Fangyu Hong +15

Huawei Technologies Co., Ltd.

Reinforcement Learning Rubric-Based RL Reinforcement Learning with Verifiable Rewards RL for VLMs

May 28, 2026cs.LG

HPO: Hysteretic Policy Optimization for Stable and Efficient Training under Sparse-Reward Regime

We investigate a narrow but common failure mode of GRPO-style reinforcement learning in the context of sparse verifiable rewards: early updates contain more responses with negative advantages than those with positive advantages, while response-level length normalization ties the magnitude of the update to the length of the output. We propose Hysteretic Policy Optimization (HPO), a minimal modification of GRPO that reduces the weight of negative-advantage updates and replaces per-response length normalization with mean-length normalization. We further introduce Adaptive HPO (A-HPO), which sets the hysteretic weight based on batch-level advantage-sign statistics, thereby removing the need for tuning a fixed hysteretic weight. In our TeleLogs and Countdown experiments, A-HPO improves the reward per update compared to GRPO, with the largest gains in early sparse reward regimes. On TeleLogs, A-HPO achieves a final reward of 0.84, outperforming SAPO by 5%, GSPO by 11%, and GRPO by 15%, while maintaining a comparable response-length. On Countdown, A-HPO achieves the largest gains in initial and most difficult configurations across 1.5B-7B models. Ablation studies on the hysteretic weight show that the gains of A-HPO come from better balancing the contributions of positive and negative advantages compared to positive-only or fully symmetric updates.

Mohamed Sana, Nicola Piovesan, Antonio De Domenico +2

Paris Research Center, Huawei Technologies, Boulogne-Billancourt, France · Huawei Technologies, China

Group Relative Policy Optimization Policy Optimization Reinforcement Learning with Verifiable Rewards RL Post-Training Sparse-Reward RL Policy Learning

May 28, 2026cs.LG

RL2ML: Finite-Rollout Surrogate Objectives from Reinforcement Learning to Maximum Likelihood

Correctness-based Reinforcement Learning with Verifiable Rewards (RLVR) trains language models from binary feedback on sampled outputs, but the objective optimized in expectation and the stochastic update geometry induced by finite rollout groups are often conflated. This paper develops RL2ML, a family of finite-rollout surrogate objectives with a closed-form, exactly unbiased gradient estimator. The family continuously connects standard reinforcement learning, maximum-likelihood-like training, and beyond-maximum-likelihood objectives while preserving estimator-objective alignment under a fixed rollout budget. We introduce the group-level update scale to characterize how a rollout group is reweighted after its empirical success count is observed, revealing a subcritical-supercritical update-scale transition that is hidden by population-level objective notation alone. Building on this distinction, calibrated metric-gain analysis and exact variance decomposition show that the best choice of surrogate objective is determined neither by proximity to maximum likelihood nor by the population-level weight alone. Instead, it depends jointly on the evaluation metric, local sensitivity, and estimator variance. The remaining degree of freedom in the surrogate objective family can therefore be formulated as a one-dimensional optimization problem rather than treated as an unconstrained hyperparameter.

Yifu Zheng

University of Southern California

RL for Language Models Policy Gradient Reinforcement Learning Reinforcement Learning with Verifiable Rewards

May 28, 2026cs.CL

Verifiable Rewards Beyond Math and Code: Lightweight Corpus-Grounded Process Supervision for Factual Question Answering

Applying reinforcement learning to improve factual accuracy in knowledge-intensive question answering faces a reward design dilemma. Response-level rewards provide only coarse supervision and cannot distinguish correct from incorrect statements within a reasoning trace. Sentence-level alternatives offer finer-grained feedback, but typically rely on NLI verifiers, LLM judges, or knowledge-verification pipelines that are expensive to deploy at RL scale and often unreliable for rare-entity facts, where accurate reward signals are especially important. We propose CorVer (Corpus Verify), a lightweight, plug-in-ready process reward that replaces neural verifiers with a corpus-grounded signal derived from Wikipedia co-occurrence statistics. CorVer assigns sentence-level credit and maps it to token-level advantages via a simple alignment, requiring only a 0.5B extractor and a single corpus lookup per sentence. Across 30 (model, benchmark) cells spanning six instruction-tuned models (3B to 14B) and five QA benchmarks, CorVer improves over the raw baseline for every cell, with an average TriviaQA gain of +4.1 pp. It also outperforms four neural-verifier baselines in 18 of 20 cells under their feasible configurations, while training 4.8 to 8.4x faster.

Shicheng Fan, Haochang Hao, Dehai Min +3

University of Illinois Chicago

Process Reward Models RL for Language Model Reasoning Automated Fact-Checking Reinforcement Learning with Verifiable Rewards Knowledge-Intensive QA

May 28, 2026cs.CL

Prompt-Level Reward Specifications for Open-Ended Post-Training

Open-ended post-training benefits from rewards that make prompt-specific success conditions explicit, rather than relying only on post-hoc scalar scores. In instruction following, writing, and decision-support tasks, response quality depends on local requirements, holistic preferences, and explicit constraints, but existing reward methods often leave these criteria implicit or cover only narrowly verifiable cases. We propose a prompt-level reward specification framework that separates reward specification from reward computation. Given only prompts, our framework constructs reusable task-adaptive rubrics and executable hard-constraint checkers offline, making reward criteria explicit before training and reusable across rollouts. At scoring time, artifact-anchored rubric and code scores are combined with an independent global score for residual holistic quality, yielding a normalized hybrid reward over requirement satisfaction, holistic quality, and deterministic constraints. The framework requires no human preference annotations, reference answers, or a separately trained reward model. Experiments show that the resulting reward improves offline RM-style response ranking and supports online reinforcement learning across multiple open-ended benchmarks. Ablations further show that rubrics, global scoring, and executable verification provide complementary supervision.

Zijun Weng, Xiaohui Hu, Shuangyong Song +3

1Fudan University · 2Xingchen AGI Lab, China Telecom Artificial Intelligence Technology (Beijing) Co., Ltd.

Open-Ended Generation Reward Modeling Reinforcement Learning Rubric-Based RL Reinforcement Learning with Verifiable Rewards RL Post-Training+1

May 28, 2026cs.LG

When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer

Reinforcement learning using verifiable rewards (RLVR) improves LLM reasoning, but the conditions under which it transfers across domains -- and why it does so -- remain under-explored. We study cross-domain transfer in a 7B model whose SFT and RL post-training stages use only constraint-satisfaction puzzles, with no mathematics problems in the post-training data. To analyze how transfer emerges, we introduce a reasoning primitive-level framework that combines a 9-class span classifier with motif extraction, allowing us to segment chain-of-thought traces into primitive motifs and track their evolution across training stages and domains. We find that puzzle SFT induces a reasoning-primitive vocabulary, yielding a

+7

pp \texttt{pass@32} gain on OlymMATH-Hard. Vanilla GSPO then composes these primitives into longer compute-verify chains, adding a further

+6

pp. However, this RL stage also suppresses exploratory primitives such as \textit{hypothesize} and \textit{backtrack}. To address this, we introduce a novelty bonus that rewards diverse correct rollouts, using perplexity under the reference model as a signal. This restores recovery primitives during RL and adds a further

+7

pp \texttt{pass@32} relative to vanilla GSPO. Finally, the end-to-end recipe raises the hard-math capability ceiling from

16.0\%

at the OLMo3-7B-Instruct-SFT base to

36.0\%

, without adding any mathematics problems during the SFT or RL stages.

Mayug Maniparambil, Arjun Karuvally, Terrence Sejnowski +1

Fin AI Research · Salk Institute for Biological Studies

RL for Language Models RL for Language Model Reasoning Cross-Domain Transfer Learning Reinforcement Learning with Verifiable Rewards LLM Mathematical Reasoning

May 27, 2026cs.CL

OmniVerifier-M1: Multimodal Meta-Verifier with Explicit Structured Recalibration

Visual outcomes are increasingly central to multimodal large language models, making reliable and fine-grained verification essential for scaling generalist foundation models. In this work, we investigate multimodal meta-verification, which leverages verifier-generated rationales rather than decision-only signals, and explore how to effectively incorporate meta-verification feedback into multimodal verifier training. We identify two key findings. First, symbolic verifier outputs (e.g., bounding boxes) outperform textual explanations as meta-verification rationales, enabling efficient rule-based reinforcement learning rewards while avoiding reliance on model-based rewards from auxiliary judge models. Second, decoupling reinforcement learning objectives for binary judgment and meta-verification substantially outperforms joint reward optimization, due to intrinsic differences in output structure and learning dynamics. Based on these insights, we train OmniVerifier-M1, a generalist visual verifier leveraging symbolic meta-verification and decoupled reinforcement learning. OmniVerifier-M1 provides robust verification and fine-grained error localization, and further enables M1-TTS, a verifier-driven agentic generation system achieving dynamic region-level self-correction. This approach paves the way for more reliable, interpretable, and fine-grained multimodal verification, supporting safer and more controllable foundation model deployment.

Xinchen Zhang, Bowei Liu, Jiale Liu +7

Tsinghua University · Pennsylvania State University · University of Southern California +2

Multimodal Large Language Models Reinforcement Learning with Verifiable Rewards Multimodal Foundation Models Multimodal Model Evaluation