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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Latest papers 438

Jul 31, 2026cs.LG

Verifier-Induced Support Reshaping in On-Policy Optimization

We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce. We call this verifier-induced support reshaping and define effective rewardable support as successful trajectories reachable within a fixed rollout budget. Across two model families, we study this effect through repeated verifier-scored sampling and bidirectional training on mathematical reasoning and constrained instruction following, including sequential training with the opposite verifier. Math-RLVR raises average instruction-following success but reduces the number of prompts with any successful response under repeated sampling. On IFEval with Qwen3-8B-Base, pass@1 rises by 6.5 percentage points while best@32 falls by 9.8 percentage points, and the same divergence appears across both models and IF benchmarks. Conversely, IF-RLVR shifts math responses from step-by-step openings toward direct answers, lowers best@k across sampling budgets, and reduces reward variation for later Math-RLVR. Token-distribution analyses and controlled opening interventions show that these changes concentrate in the first few response tokens. RLVR mainly reranks openings already available in the base policy, and the selected opening causally affects math searchability. The tested reference-policy constraints, routing priors, and on-policy distillation preserve cross-task support only partially; MathIF and ReasonIF show that marginal gains translate only partly into responses that are both correct and constraint-following. Therefore, endpoint improvements do not guarantee future trainability or joint capability under on-policy optimization. Code is available at https://github.com/sylvain-wei/VISR

Shaohang Wei, Zikun Su, Feifan Song +4

Peking University · BUPT

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

Jul 31, 2026cs.LG

SAF-OPD: Stable Advantage Fusion for On-Policy Distillation

Reinforcement learning with verifiable rewards (RLVR) broadcasts a single response-level reward to every token, while on-policy distillation (OPD) scores each token against a stronger teacher for a dense advantage but caps performance at teacher quality and discourages exploration beyond it. Their complementarity makes combining RLVR and OPD promising, but we find that fusing the two advantages with a fixed coefficient triggers entropy collapse from two miscalibrations: a magnitude mismatch, where token-level OPD advantages can spike far beyond the bounded RLVR advantage and erase its signal, and a temporal mismatch, where sustained full-strength OPD keeps pulling the student toward the teacher and limits exploration needed to surpass it. We propose SAF, a Stable Advantage Fusion framework that resolves both issues via a lightweight, four-stage pipeline applied only to the OPD advantage: a sparsify-then-compress mechanism for magnitude control paired with a warm-up-then-anneal mechanism for temporal control, with each stage independently switchable and adding negligible overhead. Instantiating RLVR with GRPO, we evaluate SAF across seven mathematical reasoning and code generation benchmarks with Qwen3-1.7B/4B/8B: SAF avoids entropy collapse and consistently outperforms fixed-coefficient GRPO+OPD fusion, improving the aggregate score by 0.51-2.70% across all six model-domain settings while achieving more stable training.

Yifan Ding, Xincheng Wei, Yoshua Y. Li +7

Shanghai University of Finance and Economics · Meituan, LongCat Team · The Chinese University of Hong Kong, Shenzhen +1

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards On-Policy Distillation

Jul 30, 2026cs.CL

LEEPS: Latent-Guided Explore-Exploit Prompt Sampling for Efficient RLVR in Large Language Models

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models, but prompt groups with identical rollout rewards consume generation budget without effective learning signals. Pre-rollout prompt selection can reduce this waste by screening prompts before rollout generation. However, existing pre-rollout methods struggle to balance exploitation and exploration: repeatedly exploiting historically informative prompts can narrow training coverage, whereas broader exploration can lower the fraction of informative prompts. To address these limitations, we introduce LEEPS, a Latent-Guided Explore--Exploit Prompt Sampler that adaptively balances the reuse of previously observed informative prompts with continued exploration of uncertain ones. LEEPS partitions candidates into exploit and explore portfolios and adaptively allocates rollout budget according to their recent non-trivial ratios. It further uses representation-space neighbors and historical rollout outcomes to prioritize uncertain prompts likely to yield non-zero reward variance, thereby making exploration more targeted without additional rollouts. Across six mathematical reasoning benchmarks, LEEPS achieves the highest average score at both model scales, with relative gains of 2.6% and 3.7% over the strongest baseline for Qwen2.5-Math-1.5B and 7B, respectively, and generally improves faster during the training process. It also achieves the highest average score across the three evaluated OOD general-reasoning benchmarks at both model scales and adds only about 2 seconds of online sampling overhead per training step. Code is available at https://github.com/ShuangLiangX/LEEPS.

Shuang Liang, Haoyang Zhou, Yifan Gong +2

Renmin University of China · AntGroup

Numerical Reasoning in Language Models Reinforcement Learning with Verifiable Rewards Sample-Efficient RL

Jul 30, 2026cs.AI

Group-Reflective Self-Distillation for Agentic Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language model agents. However, terminal rewards provide only coarse trajectory-level supervision, leaving successful behaviors, recurring mistakes, and incidental choices entangled in the same outcome signal. Existing agentic self-distillation methods enrich sparse supervision with natural-language skills, but skills retrieved externally or extracted from a single trajectory by stronger models may mismatch current experience, exceed the policy's capability, or remain path-specific. We propose Group-Reflective Self-Distillation (GRSD), which derives capability-aligned and outcome-discriminative guidance from the policy's own verified rollouts. For each prompt, the policy reflects on each verified trajectory in an on-policy group, and a stop-gradient snapshot contrasts the resulting reflections from successful and failed rollouts to construct group-level privileged guidance. Conditioned on this guidance, a self-teacher refines turn-level credit assignment by modulating outcome-based advantages while preserving the verifier-determined learning direction. Experiments across multiple agentic environments and model scales demonstrate that GRSD consistently outperforms competitive baselines and generalizes more effectively to unseen tasks.

Binbin Zheng, Zijun Xie, Guanqun Zhao +4

University of Science and Technology of China · 2Baidu Inc. · 3Peking University +3

Agentic RL Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Self-Distillation

Jul 30, 2026cs.LG

Beyond Binary Rewards: A Comparative Study of Reward Design for Reinforcement Unlearning

Machine unlearning seeks to selectively remove specific knowledge from trained language models without full retraining, a growing necessity under privacy regulations such as GDPR and the EU AI Act. Recent work has reformulated unlearning as a Reinforcement Learning with Verifiable Rewards (RLVR) problem, where models are optimized against verifiable rewards computed directly from their outputs. However, existing methods rely on sparse binary rewards that provide minimal learning signal, indicating only whether forbidden content was avoided, and limiting convergence speed. In this paper, we study how reward design affects unlearning efficiency within the Reinforcement Unlearning (RUL) framework. We introduce a principled reward decomposition framework that decouples verifiability from sparsity, and propose two new reward functions: an exponential reward that provides graded penalties based on the count of forbidden-concept occurrences, and a PageRank inspired reward that weights penalties by semantic importance. We conduct experiments on the Real World Knowledge Unlearning (RWKU) benchmark, demonstrating that both rewards consistently outperform the binary setting, while reaching similar forgetting performance up to

3\times

faster and preserving general model utility. Our results show that reward design is a key driver of unlearning efficiency offering a practical path toward scalable and efficient machine unlearning.

Efstratios Zaradoukas, Davide Gabrielli, Bardh Prenkaj +1

Technical University of Munich, Germany · Munich Center for Machine Learning, Germany · Sapienza University of Rome, Italy

Reinforcement Learning with Verifiable Rewards Machine Unlearning Reward Design for RL LLM Unlearning

Jul 30, 2026cs.AI

Not All Tokens Deserve Equal Credit: Counterfactual Sensitivity Credit Reallocation for Long-CoT Reasoning

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

Qiangqiang He, Zhongheng Wu, ZiJian Wang

State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · Institute of Wireless Communications Technology, Shanghai Jiao Tong University, Shanghai, China

Token-Level Credit Assignment RL for Language Model Reasoning Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Counterfactual Credit Assignment LLM Reasoning

Jul 30, 2026cs.LG

LoRA Scaffolded Policy Optimization (LSPO): A Sampling-Time Low-Rank Scaffold for Recovering Reinforcement-Learning Gradient on Zero-Reward Cliff Prompts

Reinforcement learning from verifiable rewards (RLVR) for mathematical reasoning suffers from a structural blind spot: on "cliff" prompts-those on which every sampled rollout in a group fails-the group-normalized advantage is identically zero, so GRPO produces no gradient on precisely the prompts at the frontier of the model's capability. We introduce LoRA Scaffolded Policy Optimization (LSPO), a sampling-time mechanism that recovers this lost gradient. Each RL step, LSPO detects cliff prompts, fits a small low-rank (LoRA) adapter by a brief supervised step on their ground-truth solutions, re-rolls the cliffs with the base-plus-adapter model, splices the now-successful completions back into the RL batch with an importance-sampling correction, and takes a GRPO step on the base alone; the adapter receives only the supervised gradient and is discarded at checkpoint, yielding a base-only model. On DeepMath-103K with DeepSeek-R1-Distill-Qwen-1.5B, evaluated over n=5 paired seeds per arm at a matched 1000-step reporting horizon, LSPO's 5-seed mean matches or beats a DAPO baseline on all 16 (benchmark, pass@k) cells (15 strict wins and one exact tie), with gains of up to +10.7 points on AIME24/pass@4, +6.7 points on AIME24 and AIME26 at pass@16, and +2.4 points on MATH500/pass@1; averaged over the 16 cells the improvement is +3.8 points.

Ken Ding

NVIDIA

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

Jul 29, 2026cs.CR

Graph Is the Verifier: Agentic Reinforcement Learning for Interprocedural Vulnerability Detection

Real-world vulnerabilities often span multiple functions, yet most learning-based detectors classify each function in isolation: on a sample of real CVEs, we find that 71.7% of vulnerable functions require evidence from outside the function to be classified correctly. Agentic reinforcement learning (RL) could close this gap by enabling a model to gather that evidence itself, but it lacks a reliable reward, since a reward defined on the final verdict alone can be obtained without performing any investigation. We propose VulAgentRL, an agentic RL framework for interprocedural vulnerability detection built on a Code Property Graph (CPG). The CPG serves two roles: at inference time the policy queries it for callers, callees, dataflow, and other queries, and at training time the same graph verifies the evidence the policy cites. Because every CPG node carries a persistent integer identifier, this verification is an exact comparison rather than a textual match, so the reward credits verdicts that are supported by evidence. We further initialize the policy by distilling teacher investigations, and show that this warm start is necessary, since RL cannot acquire tool-use behavior it never samples. Under a repository-level split that prevents leakage, VulAgentRL outperforms state-of-the-art baselines, including frontier models, on the strict pair-wise-correct metric while issuing fewer tool calls, and its advantage persists on an out-of-distribution corpus and under class imbalance.

Yikun Li, Ting Zhang, Jiakun Liu +9

1Singapore Management University, Singapore · 2Harbin Institute of Technology, China · 3GovTech, Singapore

Agentic RL Software Vulnerability Detection Reinforcement Learning with Verifiable Rewards

Jul 29, 2026cs.LG

DHRCL:Training Code LLMs with Dense Hierarchical Rewards and Curriculum Learning

Reinforcement learning is a natural post-training paradigm for code-oriented large language models because generated programs can be evaluated through parsing, execution, unit tests, and structural analysis. However, existing methods often rely on sparse outcome rewards or statically combine heterogeneous dense signals, even though syntax validity, executability, functional correctness, and structural organization describe different and progressively dependent programming capabilities. We propose DHRCL, a reinforcement learning framework with Dense Hierarchical Rewards and Curriculum Learning. DHRCL decomposes feedback into syntax validation, execution success, unit-test pass rate, and AST-based structural similarity, and organizes these signals through a three-stage Syntax, Execution, Pass & Structural curriculum. Stage duration is determined automatically from recent validation trends rather than manually specified capability thresholds. We further introduce stage-aware probability-based token credit redistribution. The mechanism follows a consolidation-to-refinement principle: it emphasizes established token patterns during syntax-oriented optimization, applies uniform propagation for non-local execution feedback, and allocates more credit or blame to less-established token decisions during final functional optimization. Under a unified Qwen3-8B and KodCode protocol, the experiments compare DHRCL with binary, pass-rate, reward-model-based, and verifiable dense-reward baselines. We further evaluate DHRCL across Qwen3-4B, Qwen3-8B, and Qwen3-14B backbones, showing that its advantage remains consistent as model capacity increases.

Shuhang Wang, Ziming Li, Hui Cheng

RL for Code Generation Reinforcement Learning Credit Assignment in RL Dense Reward RL Curriculum RL Reinforcement Learning with Verifiable Rewards

Jul 28, 2026cs.LG

Early Verdicts, Better Budgets: Sequential Adaptive Rollout Allocation for Compute-Efficient RLVR

Reinforcement learning with verifiable rewards (RLVR) is bottlenecked by rollout generation, yet many sampled prompts produce saturated groups (all responses correct or all incorrect) whose zero reward variance yields no policy-gradient signal. Existing remedies either oversample a larger candidate pool and discard saturated prompts (dynamic sampling), paying heavy extra rollouts, or predict prompt difficulty before sampling, which is fragile under a shifting policy. We observe that a group's effectiveness is usually decided early, within the first few of its rollouts, so spending a full group on an already-decided prompt is wasteful. We cast per-step rollout collection as a budget-constrained sequential allocation (optimal stopping) problem and introduce SARA (Sequential Adaptive Rollout Allocation). SARA maintains a Beta posterior over each prompt's success rate, evaluates a closed-form predictor of group effectiveness, and applies a two-threshold, SPRT-style rule that commits effective groups, abandons saturated ones after a short probe, and reallocates the freed budget to fresh prompts, without any extra prediction rollouts. We prove abandonment reliability, expected rollout savings, fixed-budget yield dominance, and a link between effective-group yield and the GRPO gradient norm. On mathematical reasoning and planning with 1.5B/3B models on a single GPU, SARA matches DPS (both below the DS oracle) while using 22% fewer rollouts than DS; composing SARA with DPS yields the best accuracy, slightly above DS, at 67% fewer rollouts (near-uniform cost).

Pixel Nomand, Elena Voss, Marcus Hale +1

University of Wisconsin–Madison · University of Washington

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

Jul 28, 2026cs.LG

Reinforcement Learning for Code Optimization

RL for code correctness is now established: have the model generate a program, run it against hidden test cases, and reward solutions that pass. Extending this to code optimization seems straightforward: just add execution time to the reward. But in practice, once timing drives the reward, small problems in measurement noise, reward sparsity, or GRPO instability overwhelm the signal and make RL fail: generated solutions are barely faster, and more of them can fail. We make execution time learnable through three stages: (1) how code is tested, by building DMC-Optim with large optimization tests and a calibrated sandbox; (2) how speed is turned into reward, by composing correctness and speed in the RL environment and using an offline simulator to predict the most promising configurations; and (3) how the model learns from that reward, by adapting GRPO and evaluation to the sparser, noisier timed-execution setting. On DMC-Optim, the strongest optimization-aware configurations improve strict top-50% pass@1 from 18.0% to 31.3% on Qwen 2.5 7B and from 30.7% to 50.4% on CWM 32B. These gains further increase at stricter percentiles such as top-30%, with 125% relative improvement for CWM 32B, while preserving pure-correctness scores. When the timing sandbox is degraded, robust optimization RL reaches 100% to 200% improvement over standard RLVR, depending on the evaluation criterion. On LCB, CWM 32B wins up to 83% of median-sample speed comparisons against standard RLVR. Relative to the fastest correct human submissions per problem, it reaches about half the human rate of complexity-class improvements (13% vs. 22%).

Pierre Chambon, Kunhao Zheng, Juliette Decugis +2

FAIR at Meta · Inria · Université Paris Dauphine

RL for Code Generation Reinforcement Learning Reinforcement Learning with Verifiable Rewards Robust RL Reward Design for RL

Jul 28, 2026cs.CL

CAST: Game Solvers as Turn-Level Teachers for LLM Agents

Training large language models (LLMs) to act in long-horizon games is a promising step toward generalist decision-making, yet reinforcement learning with verifiable rewards (RLVR) relies on sparse final rewards that reveal little about which decisions determine success. Denser process signals could supply this missing turn-level credit, but existing sources are hard to keep both cheap and accurate. We observe that changes in a game solver's state value reveal whether an action advances the state toward success. Building on this insight, we propose CAST (Credit Assignment from Solver Teachers), which converts these value changes into solver advantages and injects them into RLVR as turn-level signals. We further show that, under a soft-optimal solver assumption, maximizing the solver advantage is equivalent to on-policy distillation from the solver, requiring only scalar values rather than teacher logits. Across Sokoban, Minesweeper, and Rush Hour, CAST outperforms all trained baselines on every game under both in-domain and unseen-difficulty evaluation and achieves the highest average zero-shot performance on ALFWorld and WebShop. Our code is available at https://github.com/Wloner0809/CAST.

Yu Wang, Yi-Kai Zhang, Wentao Shi +8

University of Science and Technology of China · 4Meituan, China · 2Nanjing University +1

Reinforcement Learning Game-Playing Agents Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards RL for LLM Agents

Jul 27, 2026cs.AI

EviBack: Search-Agent Reinforcement Learning via Evidence-Constrained Teacher Backoff

Reinforcement learning enables Agentic RAG systems to learn multi-turn search from verifiable outcome rewards, but all- zero rollout groups provide no comparative signal and may hide useful search behavior. We present EviBack, an evidence- constrained Teacher backoff that supplies auxiliary super- vision to such groups while preserving verifiable Actor re- wards. It separates evidence assessment from answer refine- ment, preventing reference answers from overriding evidence- insufficiency judgments. A fully automated, end-to-end GPT- 5.5-assisted APE pipeline starts from a manually authored single-prompt dual-task Teacher, automatically partitions and labels rollout data, and performs ablation, task decomposition, evaluation, and selection to produce a gated two-stage Teacher. Compared with the manual design, the resulting Teacher im- proves downstream F1 and valid-answer rate while reduc- ing search, duplicate queries, and forced termination. Across seven open-domain QA benchmarks and three Qwen3 scales, EviBack improves F1 over Search-R1 and raises both single- and multi-hop macro F1. We guarantee that the code will be made publicly available at a later stage.

Xiao Ma, Zhiquan Hu, Yi Wei +5

NEXTAI Research Institute, Chery Group

Reinforcement Learning Agentic RAG Reinforcement Learning with Verifiable Rewards RL for LLM Agents Open-Domain QA

Jul 26, 2026cs.AI

From RLVR to RLSVR: Task Transformation Induces Self-Verifiable Rewards for Open-Ended LLM Self-Improvement

Reinforcement Learning with Verifiable Rewards (RLVR) has driven recent progress in reasoning-oriented large language models (LLMs) by enabling large-scale optimization. However, its applicability remains largely limited to domains such as mathematics and coding, where correctness can be deterministically verifiable. Open-ended tasks instead often rely on human preferences, reward models, or LLM-based judges, introducing evaluation bias, judge capability bottlenecks, and additional inference costs. Drawing on the principle of self-supervised learning, which constructs pretext tasks to derive supervision from the data itself, we propose Reinforcement Learning with Self-Verifiable Rewards (RLSVR), a task-transformation-based training paradigm for extending RLVR to open-ended tasks. RLSVR transforms open-ended tasks into verifiable proxy environments whose internal rules and interaction outcomes automatically generate reward signals. We instantiate RLSVR with SpyRL, a Self-PlaY Reinforcement Learning method inspired by social deduction game Who Is the Spy?. Agents receive asymmetric information, complete the same target task, and vote to identify a designated spy. Because the spy identity is predetermined, voting outcomes provide fully verifiable rewards, while successful identification remains closely related to output quality. Experiments on text summarization, creative writing, and mathematical reasoning show that SpyRL outperforms existing self-improvement methods on non-verifiable tasks and yields consistent gains on verifiable reasoning tasks. These results demonstrate that task transformation can extend scalable RLVR-based self-improvement beyond inherently verifiable domains. Models and code have been released at https://github.com/wangqinsi1/RLSVR/tree/SpyRL.

Qinsi Wang, Jing Shi, Huazheng Wang +8

Duke University · Adobe Inc. · Oregon State University +3

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

Jul 24, 2026cs.AI

Learning as Reasoning Unfolds: Progressive Rollout Allocation for Efficient Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective framework for improving LLM reasoning, with methods such as GRPO among its most successful instantiations. However, GRPO relies on repeated generation of long chain-of-thought rollouts. Training time scales with the number of rollouts, a large fraction of which are uninformative. Thus, GRPO is computationally expensive and unstable. To mitigate this, existing approaches either generate a larger pool of rollouts and filter the most informative prompts, or leverage historical signals for filtering at later stages of training. These strategies offer modest performance gains, but slow down the overall process. To address this, we propose VarIance Guided Online Rollout allocation (VIGOR) which instead of allocating a fixed rollout budget per example, begins with a small number of rollouts for all examples in a batch and iteratively allocates additional rollouts to those with the highest group reward variance until a fixed total rollout budget is reached. Theoretically, we show that under RLVR, reward variance controls the gradient magnitude, and derive VIGOR's closed-form speedup ratio over GRPO, which grows with refinement rounds under Pareto-distributed reward variance. Experiments on mathematical reasoning and coding tasks show that VIGOR reaches target accuracy with up to 2.3

\times

fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49

\times

fewer rollouts, and improves the coding average test pass rate by 3.4 points.

Heyang Jiang, Henry Liu, Baharan Mirzasoleiman

University of California, Los Angeles

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

Jul 23, 2026cs.AI

AdaKP: Online Adaptive Knowledge-Point Selection for Reasoning-Oriented Reinforcement Learning

Reinforcement learning with verifiable rewards is a powerful paradigm for eliciting reasoning in large language models, yet it suffers from severe reward sparsity on competition-level mathematics. A common remedy injects atomic knowledge points (KPs) - short natural-language hints distilled from gold solutions - into the prompt. Existing methods, however, either fix this selection once offline or merely scale the monolithic quantity of injected text, leaving untouched the most informative axis of choice: which subset of atomic KPs to inject, and when. We introduce AdaKP, an online selector that re-chooses each problem's KP subset over the course of RL training. At its core is an entropy proxy that scores a KP by the reduction in next-token entropy it induces - a single inexpensive forward pass, with a provable bound on its truncation bias - in place of expensive rollout-based estimation. Three lightweight mechanisms make this signal usable online: a momentum smoother that absorbs per-step noise, a retirement-and-revival manager that prunes weak KPs while preserving exploration, and an adaptive scheduler that front-loads re-evaluations into early training. AdaKP further contributes a pre-flight validation gate that certifies the proxy against a leave-one-out ground truth before any expensive run is launched, turning method-level risk into a falsifiable check. Realized as a fully additive fork of a standard DAPO+GRPO trainer with no optimizer changes, AdaKP improves over a strong static-selection baseline on all eight competition-mathematics benchmarks at negligible added cost, positioning online, validated KP-subset selection as a practical and as-yet under-explored axis for reasoning-oriented reinforcement learning.

Zibin Meng, Zhenyu Zhao, Chunqiang Run

The Hong Kong University of Science and Technology · University of the Chinese Academy of Sciences

Knowledge Augmentation for Language Models RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Adaptive Learning LLM Reasoning

Jul 23, 2026cs.LG

From Evaluation to Optimisation: Hierarchy-Aware Training Signals for CWE Prediction in Python

The original ALPHA benchmark introduced a taxonomy-aware penalty for evaluating CWE-level vulnerability prediction in Python and proposed that the penalty could theoretically also serve as a training signal. This paper provides that validation. We compare three delivery mechanisms: supervised fine-tuning, a dual-head classification loss, and reinforcement learning with a dense reward derived from the normalised penalty. We find that supervised approaches consistently regress below the zero-shot baseline under distribution shift, while GRPO succeeds. Our best policy reduces the cumulative ALPHA penalty of Qwen2.5-Coder-7B on Security Hardening and Adversarial Testing (SVEN) dataset by 27.9% under greedy decoding, and by 25.5% under sampled decoding(p = 0.005, Welch's t-test), reaching statistical parity with its 4.5x larger zero-shot teacher. We conclude that the value of a hierarchical penalty as a training signal depends largely on the directness of its delivery.

Muntasir Adnan, Manile Srun, Carlos C. N. Kuhn

Open Source Institute, Faculty of Science and Technology, University of Canberra, Canberra, Australia.

Software Vulnerability Detection LLMs for Cybersecurity Reinforcement Learning with Verifiable Rewards RL Fine-Tuning

Jul 23, 2026cs.LG

Multi-turn RL with Structural and Performance Aware Rewards for CUDA Kernel Generation

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful technique to enhance the reasoning capacity of LLMs for optimized code generation. However, existing RLVR approaches primarily rely on outcome-based signals such as correctness and speedup, overlooking performance-critical structural properties of programs that are essential for generating optimized code. In this work, we propose CudaPerf, a reflective RL framework that incorporates both verifiable execution rewards and structural code-aware rewards derived from parallelization features (e.g., memory coalescing, occupancy, Arithmatic Intensity, and synchronization patterns). CudaPerf operates in two stages: (1) an offline pairwise ranking module that learns to distinguish strong and weak program candidates via contrastive comparisons, and (2) an online RL training phase that jointly optimizes for correctness, performance, and structural efficiency through a unified reward signal. To further enhance learning, CudaPerf utilizes iterative refinement using execution feedback enabling progressive improvement of generated candidates. We also introduce a dataset comprising 2.9k C to CUDA and 1k PyTorch to CUDA programs, each paired with diverse input configurations and multiple CUDA implementations encompassing diverse optimization strategies. CudaPerf is evaluated across multiple benchmarks comprising both C to CUDA and PyTorch to CUDA transformations. Empirical findings suggest that CudaPerf significantly outperforms strong baselines, including Qwen-3-32B (for C to CUDA) and CUDA Agent (for PyTorch to CUDA) by achieving up to 5X & 3.32X improvements in speedup, and 17% & 7% improvements in correctness, respectively.

Quazi Ishtiaque Mahmud, Nesreen K. Ahmed, Ali Jannesari

Iowa State University, Ames, IA, USA · Cisco AI Research, San Jose, CA, USA

RL for Code Generation GPU Kernel Optimization GPU Kernel Generation Reinforcement Learning with Verifiable Rewards Reward Design for RL

Jul 22, 2026cs.CV

Trace: A Taxonomy-Guided Environment for Multidomain Visual Reasoning

Reinforcement learning with verifiable rewards (RLVR) has substantially improved language-model reasoning, yet its extension to vision-language models remains constrained by the lack of training data that are simultaneously broad, exactly verifiable, and reproducible. We introduce Trace, a taxonomy-guided environment for multidomain visual reasoning. Trace factorizes task construction into a scene grammar and an executable task program, separating visual realization from answer computation. A shared semantic state determines the rendered image, prompt, typed answer, verifier state, and replayable instance trace. The resulting environment comprises 1,000 tasks over 277 scene grammars and 11 visual domains, with controlled semantic and visual variation. RLVR on 64,000 Trace instances improves the macro-average across 24 external benchmarks by 3.51 percentage points for Qwen2.5-VL-3B and 4.06 points for Qwen2.5-VL-7B, providing evidence that broad procedural training can transfer beyond the generated task distributions. Project page: https://maveryn.github.io/trace/.

Md Tanvirul Alam

Rochester Institute of Technology Rochester, NY, USA

Synthetic Data Generation VLM Reasoning Reinforcement Learning with Verifiable Rewards RL for VLMs

Jul 22, 2026cs.CL

SLPO: Scaling Latent Reasoning via a Surrogate Policy

Reinforcement learning with verifiable rewards has become the predominant recipe for eliciting test-time scaling in explicit Chain-of-Thought reasoners. Yet this scaling path remains computationally costly, since every intermediate step must be decoded as a language token. Latent reasoning instead carries intermediate computation as continuous vectors and already matches or surpasses explicit CoT at far shorter horizons. Despite this promise, latent reasoners remain largely imitation-bound, while explicit CoT has already moved past imitation via outcome-reward RL. Latent trajectories lack a tractable per-step likelihood and an adaptive stopping interface under fixed thinking budgets, so outcome rewards cannot elicit latent test-time scaling. We introduce Surrogate Latent Policy Optimization (SLPO) to bring outcome-reward RL to autoregressive latent reasoners: an empirical surrogate policy density over latent transitions for trajectory-level credit assignment, and a correctness-supervised stopping head that outcome-reward optimization refines into a variable-horizon policy. Across continuous and soft thinking settings, SLPO improves Pass@

k

under parallel sampling and allocates longer latent computation to harder instances with higher deterministic accuracy.

Runyang You, Zhiyuan Liu, Yongqi Li +1

The Hong Kong Polytechnic University · Sichuan University · Work done as an intern at PolyU.

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Continuous Latent Reasoning Adaptive Computation Latent Reasoning

Jul 21, 2026cs.LG

ISO: An RLVR-Native Optimization Stack

Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.

Hanqing Zhu, Wenyan Cong, Zhizhou Sha +8

The University of Texas at Austin · UIUC · Emory University +3

Reinforcement Learning with Verifiable Rewards RL Post-Training Model Merging

Jul 21, 2026cs.LG

Off-Context GRPO: Learning to Reason on Hard Problems using Privileged Information

Reinforcement learning with verifiable rewards (RLVR) improves reasoning in large language models. Yet, typical RLVR approaches fail on difficult problems: when a model cannot generate any correct solutions, it receives \textit{zero} learning signal. Providing privileged guidance during training, such as solution prefixes, can help overcome this learning cliff by steering the model towards {correct solutions with non-zero reward}. {We call these rollouts \textit{off-context}: they are generated from a training prompt that contains privileged guidance, while the target objective is defined by the original prompt without that guidance.} {We introduce} Off-Context GRPO (OC-GRPO), a minimally modified variant of GRPO that uses guided rollouts but applies an importance-corrected objective to steer the update back toward the original unguided objective, avoiding the mismatch that destabilizes uncorrected guided training. Empirically, our algorithm achieves a 3.9% absolute improvement (13.8% relative gain) over vanilla GRPO on average across standard mathematical reasoning benchmarks with negligible additional cost.

Priyank Agrawal, Ankur Samanta, Shervin Ghasemlou +4

1Meta AI · 2Columbia University · *Work done at Meta

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

Jul 21, 2026cs.CL

The Price of Reasoning: Cost-Quality Tradeoffs in Reinforcement Learning for Neural Machine Translation

Reinforcement learning with verifiable rewards (RLVR) has been established as a viable paradigm for the post-training of Large Language Models (LLMs), including downstream tasks, such as Neural Machine Translation (NMT). With the latest research indicating that RLVR could be the preferred training method for translating legal documents due to the induced reasoning capabilities, it raises the question whether it is really attributed to the reasoning or more generally to the training paradigm. We investigate the importance of including the model's reasoning trace in the generated responses during both training and inference by systematically omitting it from one of the phases. Our experiments show that including the reasoning, specifically during inference, has a positive effect on the overall translation quality. Furthermore, we recognise that the reasoning leads to an increase in output tokens, hence we study the cost-quality tradeoff between the increased computational demands and the improved translation quality.

Michael Jungo, Aixiu An

AIBEX, University of Fribourg Fribourg, Switzerland · iCoSys, University of Applied Sciences and Arts Western Switzerland Fribourg, Switzerland

RL for Language Models RL for Language Model Reasoning Efficient Language Model Reasoning Reinforcement Learning with Verifiable Rewards Machine Translation

Jul 21, 2026cs.LG

Adopting Reinforcement Learning with Verifiable Rewards for Molecular Generation

Leveraging large language models (LLMs) for molecular generation has shown remarkable potential in chemical and drug design. Current methods primarily rely on supervised training or fine-tuning with limited datasets, which are insufficient to capture complex molecular design objectives. While some approaches attempt to guide generation toward specific goals, they often lack direct optimization mechanisms, making it difficult to align generated molecules with desired properties. To tackle these challenges, we propose \textbf{LLMol}, a principled reinforcement learning framework that directly incorporates verifiable rewards for targeted molecule generation. The key insight is to formulate molecular design as a goal-conditioned sequence prediction task, where verifiable rewards serve as explicit supervision to drive generation toward desired objectives. LLMol follows a two-stage training paradigm combining supervised learning and reinforcement learning. In the first stage, large language models are supervised fine-tuned to capture chemical syntax and molecular distributions. In the second stage, we introduce Reinforcement Learning with Verifiable Rewards (RLVR), which directly integrates property-based reward signals to guide molecular generation toward task-specific objectives. To address the high variance and instability common in discrete sequence optimization, we adopt Group Relative Policy Optimization (GRPO), a stable on-policy algorithm that smooths reward signals and improves training robustness. This framework enables LLMol to effectively handle a range of molecular design tasks, including single-property targeting (e.g., penalized logP, QED) and structure-constrained optimization. Experimental results demonstrate that LLMol consistently outperforms existing methods, achieving higher success rates and improved efficiency across diverse molecular benchmarks.

Mingxuan Ouyang, Hao Lan, Wanyu Lin

Molecular Optimization Reinforcement Learning with Verifiable Rewards Molecular Generation

Jul 21, 2026cs.LG

H $^2$ SD: Hybrid Hindsight Self-Distillation

Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but a scalar trajectory reward offers limited token-level guidance. Existing self-distillation methods add a privileged teacher but typically assign it a fixed role: direct distribution matching may destabilize successful behavior, while magnitude-only modulation offers little corrective guidance after failure. We observe that successful and failed trajectories require different forms of hindsight supervision. A successful response already contains a valid student-generated reasoning path and can therefore serve as privileged context rather than being replaced by an external rationale. A failed response, however, requires corrective reference information. We introduce Hybrid Hindsight Self-Distillation (

\mathrm{H}^{2}\mathrm{SD}

), which jointly adapts teacher context and update strategy to trajectory correctness. For successful trajectories, we construct the teacher context from the verified response and a rephrasing instruction, and use the teacher only to re-evaluate the original response tokens. The resulting probabilities refine token credit assignment without changing the direction determined by the reward. For failed trajectories, a verified reference hint provides corrective guidance through reverse-KL distillation. Experiments on challenging reasoning benchmarks show that H

^2

SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.

Qiye Cai, Yichuan Ma, Peiji Li +6

1Shanghai Artificial Intelligence Laboratory · 2Harbin Institute of Technology · 3Fudan University +1

RL for Language Model Reasoning Language Model Distillation Reinforcement Learning with Verifiable Rewards Self-Distillation

Jul 16, 2026cs.LG

Beyond Entropy: Correctness-Aware Advantage Shaping via Contrastive Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

Weiwen Xu, Jia Liu, Hou Pong Chan +4

1The Chinese University of Hong Kong · 2South China University of Technology · 3Nanyang Technological University

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

Jul 16, 2026cs.LG

Non-vacuous Generalization Bounds for Reinforcement Learning with Verifiable Rewards

While reinforcement learning with verifiable rewards (RLVR) is widely used to improve the reasoning capabilities of large language models (LLMs), the generalizability of the resulting models remains poorly understood. In this work, we establish the first non-vacuous generalization bounds for parameter-efficient RLVR fine-tuning at the billion-parameter scale. Our approach adapts PAC-Bayes compression bounds to this setting, and addresses the inherent stochasticity of token generation by applying the Gumbel-max reparameterization trick. To operationalize these bounds, we propose the Progressive RLVR framework, which integrates RLVR with on-policy distillation, TinyLoRA, and model quantization. Progressive RLVR empirically retains 84-97% performance of standard LoRA fine-tuning while producing models that are 14,796x more compressible. We show that this framework yields non-vacuous generalization bounds in four domains: mathematical problem-solving, programming, general-knowledge reasoning, and Text-to-SQL. Our bounds exceed the accuracy of the base model by 9-51% and lie within 6-11% of the accuracy of the fine-tuned models.

Yuxuan Zhu, Rohan Alur, Daniel Kang

UIUC · MIT · Bridgewater AIA Labs

PAC-Bayesian Generalization Bounds Reinforcement Learning with Verifiable Rewards RL Fine-Tuning Generalization in RL Parameter-Efficient Fine-Tuning

Jul 15, 2026cs.CV

SIVA-RL: Sensitivity-Invariance Visual Alignment for Multimodal Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) drives multimodal reasoning, but answer-level correctness does not guarantee that a vision-language model grounds its predictions in visual evidence. Existing visual-intervention methods contrast policy behavior on original and modified images, yet assign supervision by the type of intervention rather than its observed effect. This assumption fails: identical operators produce heterogeneous outcomes across samples. We propose SIVA-RL, a Sensitivity-Invariance Visual Alignment framework that replaces operator-conditioned regularization with sample-wise, outcome-conditioned supervision. SIVA-RL constructs localized interventions through token-aligned, distance-constrained within-image PatchSwap. A frozen audit policy then scores each clean-intervention pair, and the observed reward drop becomes soft routing weights. Large-drop pairs drive sensitivity alignment, low-drop pairs drive clean-anchored invariance alignment, and ambiguous pairs are down-weighted. This design decouples intervention construction from supervision assignment and is compatible with both GRPO and DAPO backbones. Across nine multimodal reasoning benchmarks spanning mathematical, logical, and vision-dependent tasks, SIVA-RL improves 3B and 7B models over matched RL baselines in every setting. It yields an 8.79 percentage-point gain on vision-dependent reasoning and up to 14.9% relative overall improvement across all four GRPO- and DAPO-based configurations.

Cheng Tang, Junzhi Ning, Min Cen +9

Shanghai Artificial Intelligence Laboratory · Shanghai Jiao Tong University · Sichuan University +2

Reinforcement Learning with Verifiable Rewards Visually Grounded Reasoning Vision-Language Alignment RL for VLMs

Jul 14, 2026cs.LG

Verifier-Based Reinforcement Fine-Tuning of Reasoning Models for Thermal Energy Storage Control

Buildings are expected to shift cooling loads in response to grid conditions. Thermal energy storage (TES) enables this shift, but scheduling it well requires planning hours ahead under storage constraints. Model predictive control (MPC) and reinforcement learning are difficult to scale across buildings. This study instead adapts an open-weight reasoning model through reinforcement learning with verifiable rewards (RLVR). We convert exact offline dynamic-programming (DP) action values into dense rewards for every candidate action. Using only 30 training prompts, reinforcement fine-tuning (RFT) trains the model as an upper-level scheduler that outputs hourly heat-pump setpoints from text-based states and forecasts. Evaluation uses a deliberately simple office-building TES benchmark where exact DP is tractable and the optimum is known. RFT reduces the open-weight model's emissions from 70.5 to 61.2 kg-CO2, close to the DP optimum of 60.8 kg-CO2. GPT-5 nearly matches DP and MPC without task-specific training, while GPT-4o, a non-reasoning LLM, produces higher emissions than the no-storage baseline, so inference-time reasoning appears important. Trace analysis shows that RFT mainly stabilizes observable planning patterns (candidate comparison, look-ahead, and feasibility checking) rather than creating a new strategy. Robustness and generalization tests clarify what transfers: the reinforced planning patterns persist under forecast errors and an unseen TES condition and carry over to a battery task, but its different structure limits the gains. DP-based verifiable rewards offer a practical way to adapt open-weight reasoning models to building storage scheduling. These results motivate higher-fidelity tests of whole-building control and scalable verifiers for city-scale energy management.

Takumi Shioda, Kohei Terashima, Tatsuo Nagai

The University of Tokyo · Tokyo University of Science

RL for Language Model Reasoning Building Energy Management Reinforcement Learning with Verifiable Rewards RL Fine-Tuning

Jul 14, 2026cs.CL

Ring-Zero: Scaling Zero RL to a Trillion Parameters for Emergent Reasoning

Reinforcement learning with verifiable rewards without human-annotated data, often referred to as zero RL, has emerged as a powerful paradigm for eliciting chain-of-thought reasoning. However, due to computational constraints, existing studies are largely restricted to small models, leaving the training dynamics and emergent capabilities at a large scale unexplored. To meaningfully explore this frontier, we aim to elicit high-quality reasoning behaviors from the model. However, we find that naive scaling often suffers from poor readability, token redundancy, and a lack of adaptive reasoning depth. To address these challenges, we present a stable and efficient training pipeline, incorporating algorithmic and system optimizations such as clipped importance sampling, training-inference ratio correction, and mixed-precision control. Our experiments offer three key findings that validate the "bitter lesson" of scaling: (1) scaling to 1T parameters significantly enhances sample efficiency and performance ceilings; (2) the training process progresses sequentially through an initial discovery phase followed by a sharpening phase; and (3) the model spontaneously develops advanced cognitive behaviors, including anthropomorphism, structured formatting, self-verification, parallel reasoning, and context anxiety, rendering hand-crafted heuristics redundant. Evaluated on seven mathematical benchmarks, Ring-2.5-1T-Zero achieves competitive performance. Additionally, to assess CoT quality beyond final-answer correctness, we propose a structured evaluation framework across three dimensions: comprehensibility, reproducibility, and efficiency, where our model demonstrates clear advantages in producing structured and concise reasoning traces. By sharing our observed emergent phenomena, we hope to provide the community with deeper insights into scaling behaviors, particularly at the 1-trillion scale.

Xinyu Tang, Qianggang Cao, Yurou Liu +13

1Gaoling School of Artificial Intelligence, Renmin University of China · 2Ant Group · 3Tsinghua University +1

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