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arXiv · 2608.29846

Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation

Run Yang·Runpeng Dai·Jie Sun·Jielei Zhang·Fan Zhou·Hongtu Zhu·Peiyi Li·Longwen Gao
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Abstract

Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teacher probabilities only for sampled tokens. Yet it frequently suffers from diversity distillation failure: the student's pass@1 improves while its pass@$k$ plateaus, failing to inherit the teacher's diversity. To explain this, we introduce First-Order Local Entropy Influence, a signed first-order proxy that decouples each update's entropy effect into the teacher--student log-probability gap and the student's local probability structure, and empirically links entropy contraction to negative-influence positions. Motivated by this, we propose Influence-Directed Adaptive On-Policy Distillation (IDA-OPD): rather than relying on costly full-vocabulary Forward-KL objectives, it preserves entropy-expanding updates while replacing entropy-contracting ones with divergence-adaptive advantage shrinkage, using only the teacher's sampled-token log-probability. Experiments on reasoning-oriented distillation show IDA-OPD consistently improves pass@$k$, inheriting the teacher's diversity through distillation, matches the strongest teacher-informed methods at strictly lower cost, and broadly maintains vanilla OPD's pass@1, all without full-vocabulary teacher information.

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Run Yang, Runpeng Dai, Jie Sun, Jielei Zhang, Fan Zhou, Hongtu Zhu, Peiyi Li, Longwen Gao. 2026-08-30. Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation. https://arxiv.org/abs/2608.29846

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