# Beyond Domain-Routed Supervision: Cross-Teacher Guarding for Multi-Teacher On-Policy Distillation

arXiv: https://arxiv.org/abs/2610.13521 · HTML: https://mlsanity.com/paper/2610.13521/

## 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 38 of its 46 references that are in the map.
- First posted on arXiv 9 Oct 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 38)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [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)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [MedXpertQA: Benchmarking Expert-Level Medical Reasoning and Understanding](https://mlsanity.com/paper/2501.18362/) (2025)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [MedReason: Eliciting Factual Medical Reasoning Steps in LLMs via Knowledge Graphs](https://mlsanity.com/paper/2504.00993/) (2025)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation](https://mlsanity.com/paper/2603.19220/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [m1: Unleash the Potential of Test-Time Scaling for Medical Reasoning with Large Language Models](https://mlsanity.com/paper/2504.00869/) (2025)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [MoDoMoDo: Multi-Domain Data Mixtures for Multimodal LLM Reinforcement Learning](https://mlsanity.com/paper/2505.24871/) (2025)
- [Open-MOPD: Diagnosing and Fixing Capability Imbalance in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2608.19098/) (2026)
- [Counteraction-Aware Multi-Teacher On-Policy Distillation for General Capability Recovery with Domain Preservation](https://mlsanity.com/paper/2605.27115/) (2026)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)

## Abstract (arXiv)

Multi-teacher on-policy distillation (MOPD) extends on-policy distillation (OPD) by routing domain-specific data to specialized teachers, integrating their capabilities through dense token-level supervision on student-generated trajectories. However, domain routing only distinguishes the supervision sources for different domains; updates from all domains still act on shared parameters. When teachers differ substantially in response style and domain expertise, supervision that is effective in isolation may still lead to persistent gradient conflicts and capability degradation during joint optimization. To address this challenge, we propose Cross-Teacher Guarding for MOPD (Road MOPD), which introduces non-routed teachers as auxiliary cross-domain critics on the same student trajectories and coordinates multi-teacher supervision through token-level credit assignment and gradient updates. Specifically, cross-teacher-guided credit assignment uses teacher agreement to strengthen token-level corrections jointly supported by the teachers and attenuate conflicting signals; preventive multi-teacher gradient projection uses auxiliary gradients from the same trajectories to constrain potentially conflicting updates and adaptively controls projection strength to retain target-domain learning signals. In experiments, Road MOPD mitigates degradation in the disadvantaged domain, gains over 5 percentage points under high conflict, and improves overall performance in low-conflict and three-domain settings.