# From Dissonance to Orchestration: Teacher Intervention in On-Policy Distillation

arXiv: https://arxiv.org/abs/2609.37510 · HTML: https://mlsanity.com/paper/2609.37510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 29 Sep 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, 19 of 19)

- [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)
- [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)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [Fast and Effective On-policy Distillation from Reasoning Prefixes](https://mlsanity.com/paper/2602.15260/) (2026)
- [Towards the Law of Capacity Gap in Distilling Language Models](https://mlsanity.com/paper/2311.07052/) (2023)
- [SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction](https://mlsanity.com/paper/2410.09008/) (2024)
- [Pass the Baton: Trajectory-Relayed On-Policy Distillation](https://mlsanity.com/paper/2607.26057/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation](https://mlsanity.com/paper/2603.22117/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) trains a student on its own reasoning trajectories using feedback from a stronger teacher. Teacher interventions can improve these trajectories, but also change the distribution on which the student learns. Our controlled studies show that rollout quality alone is an incomplete criterion for allocating teacher guidance. Deeper intervention yields diminishing gains in rollout accuracy while increasing off-policy load. In a training probe with a restricted rollout horizon, peak student accuracy and performance retention favor different intervention strengths. The preferred intervention depth and placement also vary across benchmarks. These findings motivate MAESTRO, which uses local policy disagreement to jointly adapt when the teacher takes over and how long it generates. Its policy disagreement score combines teacher-weighted candidate coverage with local distribution similarity and is aggregated within reasoning paragraphs. Across eight mathematical reasoning benchmarks, MAESTRO achieves the highest macro-average accuracy among the compared methods for both 0.6B and 1.7B Qwen3 students, with the 1.7B student leading on every benchmark. MAESTRO also reduces average training response length by 67.3% relative to standard OPD. The code is available at https://github.com/yhao-wang/MAESTRO.