On-Policy Distillation Teaches New Skills but Not New Knowledge

Abstract:On-policy distillation (OPD) strengthens language-model reasoning, yet whether students acquire new factual knowledge or compositional skill for multi-step reasoning remains unknown. We separate these capabilities using a controlled synthetic framework that measures the student's initial capabilities and independently controls the teacher's additional facts, compositional skill, or both. Across four models from three families, reverse-KL OPD reliably transfers compositional skill across unseen reasoning structures, but transfers minimal factual knowledge. Decoupling the distillation recipe reveals the source of this asymmetry: replacing reverse KL with forward KL restores factual transfer, whereas student rollouts specifically improve the execution of multi-step reasoning. Experiments on recent factual QA and competition mathematics show a similar asymmetry under reverse-KL OPD, yielding notable reasoning gains without factual memory expansion. Together, these results demonstrate that on-policy distillation does not expand a model's parametric knowledge, but instead teaches it to organize and compose the knowledge it already possesses.

Computation and Language (cs.CL)

arXiv:2610.09639 [cs.CL]

(or arXiv:2610.09639v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.09639 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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