Multi-Teacher On-Policy Distillation: Scheduling, Forgetting, and the Sampled-vs-Logit Dispute
Frontier labs distill one student from many specialist teachers at once (Nemotron 3 Ultra routes more than ten), yet nobody has published a controlled comparison of how to schedule them: routed-joint vs sequential vs sequential-with-replay, at matched token budgets, with forgetting and backward transfer measured. There is also a second open dispute, where three 2026 papers report three different winners between sampled-token and logit-distribution supervision. This study runs the clean 2×2 plus replay control at small scale, across two deliberately different domains (math and tool-calling), behind strict validity gates: pinned revisions, loss-correctness checks, and evaluator audits before anything expensive runs.
Hypothesis: Routed joint distillation gives the best multi-domain tradeoff at matched budgets, and the sampled-vs-logit winner per domain is predicted by how far student rollouts stray off the teacher's support.
