Xinzhu Chen

Xinzhu Chen, Xuesheng Li, Zhongxiang Sun et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of the popular GRPO, LESS consistently improves accuracy over strong RL baselines across three backbones and six math benchmarks, achieves stronger robustness of the performance floor.

Xinzhu Chen, Wei He, Huichuan Fan et al.

Group Relative Policy Optimization (GRPO) performs coarse-grained credit assignment in reinforcement learning with verifiable rewards (RLVR) by assigning the same advantage to all tokens in a rollout. Process reward models can provide finer-grained supervision, but they require step-level annotation or additional reward modeling. We show that hidden-state distributions contain a useful signal for local reasoning quality that can be extracted using only outcome-level correctness labels available in RLVR. Specifically, within each GRPO group, the Wasserstein distance between span-level hidden state distributions of correct and incorrect rollouts increases around regions where their local reasoning quality diverges. This association holds both across examples and within individual trajectories, suggesting that hidden-state distributional divergence can serve as a self-supervision signal for fine-grained credit assignment. We formalize this observation with a separation theorem showing that, under mild structural assumptions, post-divergence spans have larger Wasserstein distances than pre-divergence spans whenever the population-level distributional gap exceeds finite-sample noise. Motivated by this result, we propose \textbf{S}pan-level \textbf{H}idden state \textbf{E}nabled \textbf{A}dvantage \textbf{R}eweighting (SHEAR), which modifies GRPO by using span-level Wasserstein distances to scale token-level advantages, amplifying updates on tokens whose hidden states are more separated from the opposing group. The method requires no additional model and only minimal changes to the training pipeline. Experiments on five mathematical reasoning benchmarks and five code generation benchmarks show improvements over standard GRPO and strong performance relative to supervised process reward models, while requiring no additional annotation or reward model training.