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

Mayug Maniparambil, Ayush Rai, Ekansh Verma, Noel E. O'Connor, Fergal Reid

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 they localize errors and whether they push probability away from erroneous student tokens. They exhibit neither of these properties nor can they reliably distinguish correct from incorrect rollouts within the same problem. We argue that this failure is structural: locating an error in a reasoning trace is itself a search problem, while a scoring teacher is never explicitly asked to perform that search. The same model, with the same privileged information, localizes errors substantially better when allowed to generate a critique. This forms the motivation for \emph{critique-conditioned self-distillation}: first generate a critique of the…