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arXiv · 2610.19572

Divergence-Routed On-Policy Distillation for Language Models

Tiantian Peng·Guannan Lv·Hongyang Li·Qiuhe Hong·Hang Cheng·Hongjian Dou·Xiangyu Wu·Yuyang Liu
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Abstract

On-policy distillation (OPD) transfers knowledge from a teacher model to a student along student-generated trajectories, typically by minimizing the reverse Kullback-Leibler (RKL) divergence. However, RKL can provide weak corrective signals for teacher-supported tokens to which the student assigns very low probability. This raises two questions: which positions are most consequential for the behavioral gap between the student and teacher, and what additional supervision is needed at these positions? Through cross-sampling, we find that divergence-based routing more effectively pinpoints positions contributing to the teacher-student performance gap than entropy-based routing. Further analysis reveals teacher-mode under-coverage at high Jensen-Shannon (JS) divergence positions, where standard OPD increases the large teacher-student probability gaps. Motivated by these findings, we propose Divergence-Routed On-Policy Distillation (DrOPD). DrOPD retains RKL supervision at all positions and selectively adds forward Kullback-Leibler (FKL) divergence supervision at positions with high JS divergence. Experiments across six math benchmarks show that DrOPD improves over standard OPD and entropy-based routing. DrOPD also reduces severe under-coverage cases by 37.9 percent relative to OPD, supporting targeted FKL as an effective complement to OPD.

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Tiantian Peng, Guannan Lv, Hongyang Li, Qiuhe Hong, Hang Cheng, Hongjian Dou, Xiangyu Wu, Yuyang Liu. 2026-10-14. Divergence-Routed On-Policy Distillation for Language Models. https://arxiv.org/abs/2610.19572

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