arXiv AI By Jie Zhang, Jingxiao Yang, Zhehao Huang, Yuhang Liu, Xiaolin Huang

When and Where to Trust the Teacher: Unifying On-Policy Distillation and GRPO through Entropy-Calibrated Credit Assignment

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The paper introduces UECR-GRPO, a method that unifies on‑policy distillation and verifier‑based reinforcement learning for mathematical reasoning. It combines verifier rewards and teacher‑derived log‑ratios into a single KL‑regularized objective (Path‑Utility Unification) and then redistributes credit at the token level using entropy‑calibrated redistribution, preserving total task credit. Experiments on five benchmarks show that UECR‑GRPO improves average accuracy by up to 0.89 percentage points over the best baseline for both Qwen3‑1.7B and Qwen3‑4B students.

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