OPRD: On-Policy Representation Distillation

Abstract:On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: this https URL.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2606.06021 [cs.LG]

(or arXiv:2606.06021v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.06021 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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