SEAD: Competence-Aware On-Policy Distillation via Entropy-Guided Supervision

SEAD uses entropy-guided supervision at token, phase, and prompt levels to cut wasteful gradients and achieves +4.8 average accuracy over vanilla on-policy distillation.

Michael Lee, Zelei Cheng, Yu Wang, Renkun Ni, Sambit Sahu, Shi-Xiong Zhang, William Campbell

Published 2026Sydney Poster Session 6 · Thu, Dec 10, 5:00 PM–8:00 PM local time · Hall 1-4arXiv ↗OpenReview ↗

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Abstract

On-policy distillation (OPD) has a property absent in offline distillation and RL: teacher supervision quality depends on student competence. Incoherent rollouts yield noisy gradients; already-mastered tokens yield redundant ones. This creates waste at three scales (tokens, training phases, and prompts) yet existing methods supervise uniformly. We introduce SEAD, which uses entropy as a unified probe of this competence-dependent degradation at three scales: (1) joint teacher-student entropy partitions tokens into zones receiving tailored divergences or zero gradient (approx. 50% skipped); (2) a cosine schedule anneals from forward to reverse KL as competence grows; (3) a competence-gated curriculum introduces prompts easy-to-hard. These components are symbiotically necessary: token selection requires coherent rollouts (curriculum), annealing requires monotonic improvement (also curriculum). On OLMo-3 (7B to 32B), SEAD achieves +4.8 avg accuracy over vanilla OPD across six math benchmarks, with ablations confirming super-additive interactions.