ErrOPD: When Does On-Policy Distillation Transfer Teacher Errors?

Abstract

A distilled student can copy its teacher's mistakes along with its skills. On-policy distillation (OPD), used in recent post-training recipes, has the teacher grade every token of the student's own outputs. Which teacher errors does it pass on? We build ErrOPD, a testbed whose teachers are fine-tuned to close a JSON list one item early, an error their students almost never make. The answer depends on the KL direction: across four model families, forward-KL OPD transmits the error within the training budget (+13-23 points), while reverse-KL OPD at our reference learning rate adds under 0.05 points. A duplicated ID and, where the decision arises, two SQL errors show the same split. The reverse-KL update scales with the student's own probability of a token, and an intervention tests this: giving reverse KL forward KL's gradient magnitude at the error decision alone makes it transmit on two model pairs. Reverse-KL OPD can delay such errors rather than block them: some runs adopt the error with longer training, and Qwen3 students that already make it, even rarely, adopt it within the budget. Because greedy evaluation on Qwen3 misses the inherited error, distilled students should also be audited on sampled outputs.