Rethinking Token-Level Credit Assignment in RLVR: A Polarity-Entropy Analysis

TL;DR

This paper investigates the credit assignment problem in RLVR for LLMs by analyzing reward polarity and token entropy, proposing an entropy-aware optimization method that improves reasoning performance.

Contribution

It introduces a diagnostic tool for token analysis, adapts mutual information theory for credit bounds, and proposes EAPO, a new entropy-aware policy optimization method.

Findings

Reasoning improvements are concentrated in high-entropy tokens.

Credit bounds are upper-bounded by token entropy.

EAPO outperforms strong baselines across models.

Abstract

Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved the reasoning ability of Large Language Models (LLMs). However, its sparse outcome-based rewards pose a fundamental credit assignment problem. We analyze this problem through the joint lens of reward polarity and token entropy. Our diagnostic tool, the Four Quadrant Decomposition, isolates token updates by polarity and entropy, and controlled ablations show that reasoning improvements concentrate in the high-entropy quadrants. To justify this observation theoretically, we adapt Conditional Mutual Information to the autoregressive RLVR setting and prove that the credit a token can carry is upper-bounded by its entropy. This view yields testable predictions that reasoning gains arise primarily from high-entropy tokens, with unique roles for positive and negative updates. A gradient analysis of GRPO further reveals how uniform reward broadcast dilutes signal at high-entropy positions while over-crediting deterministic tokens. Grounded in these insights, we propose Entropy-Aware Policy Optimization (EAPO) that modulates token-level learning signals accordingly. Extensive experiments demonstrate that EAPO outperforms strong baselines across two model families.