mlsanityData to 7 Oct 2026

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

arXiv 2609.36601 ↗First posted 29 Sep 2026cs.AIcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 28 of its 36 references that are in the map. First posted on arXiv 29 Sep 2026.

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28 of 36 references.

References · 28

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2025Qwen3 Technical Reportcited by 8,195
  3. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  4. 2023Let's Verify Step by Stepcited by 3,598
  5. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,678
  6. 2022Fast Inference from Transformers via Speculative Decodingcited by 1,615
  7. 2020Knowledge Distillation: A Surveycited by 1,578
  8. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,359
  9. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  10. 2023Accelerating Large Language Model Decoding with Speculative Samplingcited by 975
  11. 2023On-Policy Distillation of Language Models: Learning from Self-Generated Mistakescited by 840
  12. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
16 more
  1. 2016Sequence-Level Knowledge Distillationcited by 761
  2. 2013Do Deep Nets Really Need to be Deep?cited by 466
  3. 2018Blockwise Parallel Decoding for Deep Autoregressive Modelscited by 318
  4. 2026Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipecited by 262
  5. 2026Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolationcited by 157
  6. 2024Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Samplingcited by 85
  7. 2026Your Group-Relative Advantage Is Biasedcited by 32
  8. 2026Trust Region On-Policy Distillationcited by 26
  9. 2026CDRRM: Contrast-Driven Rubric Generation for Reliable and Interpretable Reward Modelingcited by 10
  10. 2026Draft-OPD: On-Policy Distillation for Speculative Draft Modelscited by 10
  11. 2025ResT: Reshaping Token-Level Policy Gradients for Tool-Use Large Language Modelscited by 9
  12. 2026Trust-Region Behavior Blending for On-Policy Distillationcited by 7
  13. 2026Weak-Driven Learning: How Weak Agents make Strong Agents Strongercited by 5
  14. 2026When Self-Belief Misleads: Active Label Acquisition for Reinforcement Learning with Verifiable Rewardscited by 5
  15. 2026ZipRL: Adaptive Multi-Turn Context Compression with Hindsight Response Replaycited by 3
  16. 2026AMR-SD: Asymmetric Meta-Reflective Self-Distillation for Token-Level Credit Assignmentcited by 1

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  3. 2026On-Policy Distillation with Best-of-N Teacher Rollout Selection
  4. 2026Prefix-Guided On-Policy Distillation: Mining Golden Trajectories from Rollouts
  5. 2026Spend Teacher Tokens Where They Matter: Success-Referenced On-Policy Distillation
  6. 2026Reward-Gated On-Policy Distillation
  7. 2026Overcoming Scaling Limits in On-Policy Self-Distillation for LLM Reasoning
  8. 2026Interactive-Policy Distillation with Bidirectional Propose-and-Verify