Hidden States Know Where Reasoning Diverges: Credit Assignment via Span-Level Wasserstein Distance

TL;DR

This paper introduces SHEAR, a method that uses span-level Wasserstein distances between hidden states to improve credit assignment in reinforcement learning, enhancing performance on reasoning and code generation tasks.

Contribution

It demonstrates that hidden-state distribution divergence can serve as a self-supervision signal for fine-grained credit assignment without extra annotations or reward models.

Findings

SHEAR outperforms standard GRPO on reasoning and code benchmarks.

Hidden-state Wasserstein distances correlate with local reasoning divergence.

Method requires minimal changes and no additional model training.

Abstract

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.