Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning

Title:Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning

Abstract:Multi-teacher on-policy distillation (OPD) is becoming the standard way to integrate specialist capabilities into one model: train experts with RL, then distill them into the student on its own rollouts. Existing recipes assign supervision at the sequence level - each prompt goes to one domain teacher and every token receives the same weight - which implicitly assumes that a teacher is uniformly useful across a response. We find instead that useful teacher signal is sparse and heterogeneous along a reasoning trajectory, which raises a finer question: who should teach which token? Verifier-Gated Multi-Expert On-Policy Distillation (VG-OPD) answers it by verification: the counterfactual gain of an expert on a specific answer criterion licenses that expert to teach, its disagreement with the student localizes the supervision, and criterion importance sets its weight; the gated KL enters GRPO as an additive token-level advantage. Instantiated for scientific reasoning with RL-trained capability experts, VG-OPD attains the best overall performance on seven benchmarks for 4B and 8B students, ranking first on five at both scales, with the largest gains on knowledge-intensive scientific reasoning tasks. Further analysis shows that the gains come from localizing verified supervision rather than from adding teachers or distillation loss: misplacing the same supervision budget is the single most damaging change, and indiscriminate distillation drags RL below its own floor where gated distillation lifts it.

Artificial Intelligence (cs.AI)

arXiv:2609.15404 [cs.AI]

(or arXiv:2609.15404v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.15404 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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