SAKI: Maximal-Coupling-Routed Teacher Supervision for On-Policy Distillation

Abstract:On-policy distillation (OPD) reduces train-test state mismatch by training a student on its own generated trajectories, but weak students may visit teacher-misaligned prefixes where supervision is less representative. We introduce SAKI (Supervision Allocation with KL-constrained Interpolation), which combines a KL-constrained teacher-guided rollout with maximal coupling and reuses realized accept/correction events to route token-level supervision. Accepted positions retain sampled-token reverse-KL supervision, while correction positions receive direct supervision on the teacher's highest-probability token. Under maximal coupling, the correction probability is exactly TV(p_t, q_t), so the same trust-region radius controls rollout deviation and upper-bounds intervention and specialized-supervision frequency. We further implement an engine-resident speculative verifier that preserves the exact-q trajectory distribution and coupling semantics while improving matched-workload rollout throughput by 4.22x. Across seven mathematical reasoning benchmarks, SAKI improves the matched teacher-guided baseline in Mean@8 and Pass@8 for both 1.7B and 0.6B students. Placement controls and fixed-prefix analysis further support correction-triggered routing as a conflict-adaptive supervision signal.

Artificial Intelligence (cs.AI)

arXiv:2609.36601 [cs.AI]

(or arXiv:2609.36601v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.36601 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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