# Pass the Baton: Trajectory-Relayed On-Policy Distillation

arXiv: https://arxiv.org/abs/2607.26057 · HTML: https://mlsanity.com/paper/2607.26057/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 30 of its 32 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 30)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)
- [Fast and Effective On-policy Distillation from Reasoning Prefixes](https://mlsanity.com/paper/2602.15260/) (2026)
- [On the Position Bias of On-Policy Distillation](https://mlsanity.com/paper/2606.22600/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [Distilling Rule-based Knowledge into Large Language Models](https://mlsanity.com/paper/2311.08883/) (2023)

## Built on by (most cited first, 18 of 18)

- [Look Ahead Before You Distill: Future Trajectory Validation of Teacher Guidance for Agentic On-Policy Distillation](https://mlsanity.com/paper/2608.01953/) (2026)
- [When EOS Tokens Disagree: Understanding Length Inflation in On-Policy Distillation](https://mlsanity.com/paper/2609.20511/) (2026)
- [MInTRL: Off-policy Intervention can boost On-policy RL](https://mlsanity.com/paper/2609.12419/) (2026)
- [OPD-Aha: From Linguistic Momentum to Visual Reflection in Multimodal On-Policy Distillation](https://mlsanity.com/paper/2609.16459/) (2026)
- [Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation](https://mlsanity.com/paper/2609.25048/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [Interpolated Policy Distillation: A Controllable Continuum Between Off-Policy and On-Policy Distillation](https://mlsanity.com/paper/2609.37170/) (2026)
- [From Dissonance to Orchestration: Teacher Intervention in On-Policy Distillation](https://mlsanity.com/paper/2609.37510/) (2026)
- [On the Off-Policy Teacher in On-Policy Distillation](https://mlsanity.com/paper/2609.38360/) (2026)
- [Learning from Evolving Errors: Adaptive Iterative Repair for On-Policy Distillation](https://mlsanity.com/paper/2610.02700/) (2026)
- [Learning to Revise Reasoning with Segment-wise On-Policy Distillation](https://mlsanity.com/paper/2610.02703/) (2026)
- [How Should Teachers Be Prepared? RL on Student-Induced States for On-Policy Distillation](https://mlsanity.com/paper/2610.04950/) (2026)
- [On-Policy Distillation with Negative-Policy Rollouts](https://mlsanity.com/paper/2610.07874/) (2026)
- [When Do We Need On-Policy Distillation? Distilling on Offline Student Rollouts Is Often Better](https://mlsanity.com/paper/2610.11291/) (2026)
- [MetaOPD: Meta-Learned Token Weighting for On-Policy Distillation](https://mlsanity.com/paper/2610.11989/) (2026)
- [Demystifying On-Policy Distillation: Where Does the Teacher's Advantage Live?](https://mlsanity.com/paper/2610.19145/) (2026)
- [DTDD: Divergence-Triggered Dynamic Distillation for Reliable On-Policy Supervision](https://mlsanity.com/paper/2610.19302/) (2026)
- [Recovering Reliable Supervision via Critique-Guided On-Policy Distillation](https://mlsanity.com/paper/2610.20572/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) grounds token-level supervision in the student's own trajectory, yet suffers from prefix failure: once the student commits to a wrong reasoning direction, all subsequent generation builds on this deviation, producing misdirected continuations that elicit unreliable supervision and waste compute. We identify a teacher-student continuation asymmetry on failed prefixes, where the teacher tends to redirect while the student continues along the original direction, and convert it into a label-free handoff trigger in Relay On-Policy Distillation (Relay-OPD). During training, Relay-OPD constructs relay trajectories by letting the teacher briefly take over at detected trigger points to produce a teacher leg, after which the student resumes and is optimized on the resulting trajectory. A limited relay budget concentrates intervention on critical early positions while limiting departure from the student policy. With a Qwen3-4B-Instruct-2507 teacher and Qwen3-0.6B/1.7B-Non-Thinking students on eight mathematical reasoning benchmarks, Relay-OPD achieves the best or second-best results on every benchmark, outperforming standard OPD by +5.73% and the strongest baseline FastOPD by +1.49% on average for 1.7B, with consistent gains at 0.6B. Training trajectory length is reduced by over 50%.