Lujun Ji

On-policy self-distillation lets one model act as a problem-only student and as a teacher given a reference solution, but the reference pushes the teacher toward short, answer-conditioned derivations that omit exploration and self-correction. TeachBack injects a trailing slice of the reference reasoning as optional working notes and optimizes preferences in both directions: teacher trajectories should win under the problem-only prompt, while student trajectories reshape future privileged teacher rollouts. Across Qwen3-1.7B, 4B and 8B, math averages rise by 4.3, 2.2 and 2.5 points over base, and Knight-and-Knaves averages by 6.1, 3.9 and 7.5 points.

On-policy self-distillation lets one model act as a problem-only student and as a teacher given a reference solution, but the reference pushes the teacher toward short, answer-conditioned derivations that omit exploration and self-correction. TeachBack injects a trailing slice of the reference reasoning as optional working notes and optimizes preferences in both directions: teacher trajectories should win under the problem-only prompt, while student trajectories reshape future privileged teacher rollouts. Across Qwen3-1.7B, 4B and 8B, math averages rise by 4.3, 2.2 and 2.5 points over base, and Knight-and-Knaves averages by 6.1, 3.9 and 7.5 points.