A Privileged Teacher That Only Scores Cannot Search: Critique-Conditioned On-Policy Self-Distillation for Reasoning

arXiv:2610.13744v1 Announce Type: new Abstract: On-policy self-distillation promises to replace the sparse outcome signal of verifiable-reward RL with dense token-level credit: a teacher conditioned on the reference solution scores the student's own rollout, and the resulting distributional shift is distilled back into the policy. We investigate whether this scoring signal actually contains corrective credit. Using gold error spans in student rollouts, we test the two signals consumed by self-distillation objectives, the full-distribution KL and the token log-ratio, for two properties: whether

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