How Much Do Teacher Bridges Matter in Interleaved On-Policy Distillation?

Leran Chen, Zhiyuan Yao, Lingnan Kong

On-policy distillation (OPD) trains a student using teacher predictions on student-generated responses. Some methods insert teacher-written segments, or bridges, but disagree on how to train on those tokens. We compare no loss, forward KL and reverse KL on identical trajectories using Qwen3-1.7B as student and Qwen3-4B-Instruct-2507 as teacher. We separate gradients by which model wrote each token. Under our short training runs and BF16 inference, pre-specified tests detected no added accuracy benefit from teacher text as context or as a training target. A one-paragraph bridge after the student's first paragraph is only 2.7% of the tokens and contributes a small gradient nearly orthogonal to the student-token gradient. In this main comparison, the three loss treatments gave similar gradient directions and were statistically equivalent in accuracy within a +/-5 percentage-point margin. An exploratory pilot placing the bridge where failed responses disagreed most with the teacher suggested a benefit from teacher-token loss. A pre-specified replication did not confirm this, and fourfold weighting showed no significant accuracy benefit. Two limitations bound these findings. Among the…