Recovering Reliable Supervision via Critique-Guided On-Policy Distillation
Abstract
CriticOPD improves on-policy distillation by using teacher critiques to restore recoverability, enabling students to revise incorrect reasoning and achieve stronger mathematical reasoning performance.
On-policy distillation (OPD) trains a student model on its own rollouts with token-level supervision from a teacher, assuming that the teacher can reach a correct answer from any prefix the student writes. We call this property the recoverability of the teacher and show it fails on incorrect rollouts: the teacher follows student errors, although it recognizes them. We propose CriticOPD, using error recognition to restore recoverability. The teacher critiques an incorrect rollout, allowing the student to rewrite its solution following the error. The resulting output, including the critique as privileged information, is scored by the teacher while the student uses the revision without the critique for training. On two Qwen3 students and six mathematical reasoning benchmarks, CriticOPD improves OPD, with the largest gains on competition problems.
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馃 CriticOPD: Recovering Reliable Supervision via Critique-Guided On-Policy Distillation
馃攳 Key finding: Teachers can recognize student mistakes yet still follow them when continuing a flawed solution, making OPD supervision unreliable.
鉁嶏笍 Our approach: The teacher uses the reference answer to critique incorrect student rollouts, and the student rewrites the continuation with this feedback. The teacher scores the rewritten suffix with the feedback in context, while the student learns from that suffix without seeing the feedback.
馃搱 Results: Across six math reasoning benchmarks, CriticOPD improves average accuracy over OPD by 4.57 percentage points on Qwen3-1.7B and 4.06 on Qwen3-0.6B, with the largest gains on competition problems.
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