GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards
On the map: LLM reasoning → Reinforcement learning for reasoning
Abstract (arXiv)
Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 33 of its 40 references that are in the map. First posted on arXiv 3 Jun 2026.
Builds on
33 of 40 references.
Closest ancestors · 14
Same direction, newest first
- 2026Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical Reasoning12 Jan
- 2025Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs30 Nov
- 2025Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning12 Oct
- 2025OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling25 Jun
- 2025Reasoning with Exploration: An Entropy Perspective17 Jun
- 2025BNPO: Beta Normalization Policy Optimization3 Jun
- 2025DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning15 Apr
- 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
- 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
- 2025Process Reinforcement through Implicit Rewards3 Feb
- 2025The Lessons of Developing Process Reward Models in Mathematical Reasoning13 Jan
- 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations14 Dec
2 more
- 2023Let's Verify Step by Step31 May
- 2017Proximal Policy Optimization Algorithms20 Jul
Other references · 19
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
- 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,733
- 2023Lost in the Middle: How Language Models Use Long Contextscited by 3,455
- 2017Axiomatic Attribution for Deep Networkscited by 3,384
- 2022Locating and Editing Factual Associations in GPTcited by 2,691
- 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,371
- 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,392
- 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
- 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
- 2019What Does BERT Look At? An Analysis of BERT's Attentioncited by 1,003
- 2019Attention is not Explanationcited by 929
- 2019Attention is not not Explanationcited by 636
7 more
- 2018RUDDER: Return Decomposition for Delayed Rewardscited by 173
- 2024MathScale: Scaling Instruction Tuning for Mathematical Reasoningcited by 144
- 2020The elephant in the interpretability room: Why use attention as explanation when we have saliency methods?cited by 122
- 2024Dense Reward for Free in Reinforcement Learning from Human Feedbackcited by 78
- 2022Measuring the Mixing of Contextual Information in the Transformercited by 65
- 2023A Survey of Temporal Credit Assignment in Deep Reinforcement Learningcited by 59
- 2025Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimizationcited by 25
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Citing papers per year: 2026: 2.
2 papers.
Similar, not cited
Close in wording, no citation either way
- 2026Gradients Know What Outcomes Don't: Unlocking Reinforcement Learning for LLM Reasoning with Gradient-Aligned Rewards
- 2025Can GRPO Help LLMs Transcend Their Pretraining Origin?
- 2025A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce
- 2025Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening
- 2025GTPO and GRPO-S: Token and Sequence-Level Reward Shaping with Policy Entropy
- 2025Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs
- 2026Step Potential Advantage Estimation: Harnessing Intermediate Confidence and Correctness for Efficient Mathematical Reasoning
- 2026ReCo: Reweighting GRPO Against Distributional Concentration