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To prevent confidently incorrect teachers from corrupting student models under mode-seeking reverse-KL objectives, the authors develop Teacher-Gated On-Policy Distillation (TGOPD), a framework that selectively gates token-level supervision using prompt-level teacher verification. Rather than relying on unreliable distributional proxies like entropy, TGOPD evaluates teacher rollouts with an outcome verifier and dynamically routes prompts to either dense on-policy distillation or verifier-grounded GRPO. Across 4B and 35B models in math, code, and instruction following, TGOPD consistently outperforms vanilla OPD across single- and multi-domain benchmarks while boosting asynchronous teacher GPU utilization from 9.8% to 78.9%.
Because mode-seeking reverse KL aggressively amplifies incorrect teacher signals, gating dense distillation on verifier-scored teacher probes systematically outperforms uniform distillation while reclaiming massive amounts of idle teacher compute.
On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.
