Paper Detail
Qiangqiang He, Jin Li, MingCai Chen
On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher--student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged OPD, where privileged information induces larger teacher-side likelihood shifts, thereby encouraging the student to learn more of the teacher's own deviation. We introduce Calibrated On-Policy Distillation (Cal-OPD), which estimates the teacher's self-deviation region through positive and negative privileged interventions and calibrates the original teacher--student discrepancy by retaining only the component that lies beyond this region. Experiments on mathematical reasoning benchmarks show that, while retaining only about 52--65\% of the original teacher--student discrepancy as the optimization signal, Cal-OPD consistently outperforms standard OPD and its variants across model scales.
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@misc{he2026calibrating,
title = {Calibrating Teacher--Student Discrepancy for On-Policy Distillation},
author = {Qiangqiang He and Jin Li and MingCai Chen},
year = {2026},
abstract = {On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher--student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged},
url = {https://huggingface.co/papers/2609.21619},
keywords = {huggingface daily},
eprint = {2609.21619},
archiveprefix = {arXiv},
}
{}