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

• URL: http://arxiv.org/abs/2608.29846v1
• Date: Sun, 30 Aug 2026 15:22:46 GMT
• Title: Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation
• Abstract summary: We propose Influence-Directed Adaptive On-Policy Distillation (IDA-OPD)<n>IDA-OPD preserves entropy-adaptive updates while replacing entropy-contracting ones with divergence-expanding advantage shrinkage.<n> Experiments on reasoning-oriented distillation show IDA-OPD consistently improves pass@$k$, inheriting the teacher's diversity through distillation.
• Score: 17.01350720731129
• License: http://creativecommons.org/licenses/by/4.0/
• 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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