MGE-PO: Entropy-Aware Credit Assignment for Mathematical Reasoning

Jihao Huang; Guangjia Chai; Zhirui Chen; Lei Wang; Yao Liu; Liu Qi; Pengjie Ding; Xinyang Liu; Chengxun Jia; Ling Shao; Hongyu Chen; Junchen Wan

arXiv · 2610.23245

MGE-PO: Entropy-Aware Credit Assignment for Mathematical Reasoning

Jihao Huang·Guangjia Chai·Zhirui Chen·Lei Wang·Yao Liu·Liu Qi·Pengjie Ding·Xinyang Liu·Chengxun Jia·Ling Shao·Hongyu Chen·Junchen Wan

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Abstract

GRPO assigns the same group-relative advantage to equally rewarded responses within a question, leaving their generation uncertainty unused. We introduce MGE-PO, centered on four-quadrant (4Q) advantage shaping that combines verified correctness with rollout generation entropy. Correctness determines the sign of an additional correction, while entropy controls its magnitude: lower-entropy successes receive larger bonuses and higher-entropy failures receive larger penalties. An online entropy-based question curriculum supports this credit rule using cached rollout measurements. At the final checkpoint after eight training epochs on Qwen3-8B-Base, adding 4Q across three policy optimization settings yields absolute gains of 3.23-3.69% in six-benchmark macro avg@32 and 4.24-11.06% in macro pass@32. On Qwen2.5-7B-Base, the complete configuration raises four-benchmark macro avg@32 from 41.5% to 45.4%.

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BibTeX RIS

Jihao Huang, Guangjia Chai, Zhirui Chen, Lei Wang, Yao Liu, Liu Qi, Pengjie Ding, Xinyang Liu, Chengxun Jia, Ling Shao, Hongyu Chen, Junchen Wan. 2026-10-16. MGE-PO: Entropy-Aware Credit Assignment for Mathematical Reasoning. https://arxiv.org/abs/2610.23245

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