Adaptive Pullback: Reweighting Supervision at Penalty Jumps in On-Policy Distillation

Abstract

On-policy distillation (OPD) supervises student-generated responses using sampled-token student-teacher log-ratios. A positive log-ratio penalizes a token that the student assigns higher probability to than the teacher, but its current value does not distinguish sustained high penalties from abrupt increases along a response. We examine these local changes by comparing consecutive blocks of tokens within the same response. Our diagnostic identifies penalty jumps, abrupt increases in average penalty that persist on held-out tokens. Across these jumps, penalties rise while teacher confidence decreases. We call this pattern penalty-confidence tension. Boundaries into high-penalty blocks do not exhibit comparable confidence changes, showing that local changes provide information beyond the current penalty value. Motivated by this observation, we propose Adaptive Pullback OPD (AP-OPD). At each detected jump, AP-OPD uses the preceding block as a local reference and uniformly scales all supervision coefficients in the following block so that its weighted average penalty matches the preceding block's original mean. This reference determines the scaling factor without an additional strength constant. AP-OPD improves performance on both mathematical reasoning and code generation.