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On-policy distillation turned out to teach students where to branch, not just which candidate tokens to consider

AspireAI community · arXiv (cs.CL / cs.AI)
The authors argue that on-policy distillation teaches a student two different things: how to branch, meaning which candidate tokens to consider, and where to branch, meaning where to keep reasoning paths open - and that the existing token-overlap metric captures only the first. They introduce the entropy shape, the sequence of next-token entropies, to characterize the second, and propose the Entropy Shape Correlation (ESC) to measure student-teacher agreement in entropy shape. By tracking ESC through training and intervening on a teacher's entropy while preserving its token preferences, they report that where to branch causally drives distillation gains independently of how to branch. They also frame outcome prediction as a teacher-selection task and show pre-OPD ESC picks the best teacher for both students and beats existing predictors. The limitation: the causal claim is established within the authors' own experimental setup rather than across independent replications.
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