E$^2$-OPSD: Taming Entropy Overshoot in On-Policy Self-Distillation
On-policy self-distillation (OPSD) provides dense token-level supervision without a second model: one network acts as teacher with the reference solution and as student with only the problem. We identify a specific failure mode of this recipe. During training, student token entropy rises past the teacher's and remains elevated, a pattern we call entropy overshoot. We trace it to both sides of distillation. The reference-conditioned teacher is confident along its answer-directed reasoning path, but this confidence transfers poorly to student-generated prefixes, making its supervision overly tied to answer-specific cues rather than reusable reasoning patterns; meanwhile, the forward KL used...
| Authors | Yifei Liu, Minghao Fang, Xinyu Gu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 October 2026 |
| Last updated at source | 15 October 2026 |
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