SG-OPD: Sign-Gated On-Policy Distillation via Sign-Consistency Gating and Phased Teacher Sampling

• URL: http://arxiv.org/abs/2606.09304v1
• Date: Mon, 08 Jun 2026 10:11:58 GMT
• Title: SG-OPD: Sign-Gated On-Policy Distillation via Sign-Consistency Gating and Phased Teacher Sampling
• Abstract summary: On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher.<n>We propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher.<n> Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD.
• Score: 22.832360652920332
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

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