One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation
A review paper frames on-policy self-distillation collapse as governed by three levers: token weighting, privileged information, and guidance decay.
The paper critically reviews On-Policy Self-Distillation (OPSD), where a language model trains on its own generations scored token-by-token by a teacher conditioned on privileged information such as reference solutions or environment feedback. It identifies collapse, the progressive narrowing of producible reasoning paths, as the dominant failure mode and analyzes it through three levers: signal weighting, the nature of privileged information, and teacher dynamics. The review is restricted to mathematical reasoning, reports no new experiments, and offers a shared vocabulary separating settled findings from disputed ones.
- OPSD uses the model itself as a teacher via privileged information
- Collapse is identified as the field's dominant failure mode
- Three levers analyzed: token weighting, privileged information, guidance decay
- Scope limited to mathematical reasoning; no new experiments conducted
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On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2608.25936