# UP-MOPD: Update Projection in Multi-Teacher On-Policy Distillation

arXiv: https://arxiv.org/abs/2610.08398 · HTML: https://mlsanity.com/paper/2610.08398/

## 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 31 of its 39 references that are in the map.
- First posted on arXiv 6 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 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [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)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models](https://mlsanity.com/paper/2010.05874/) (2020)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [RubricHub: A Comprehensive and Highly Discriminative Rubric Dataset via Automated Coarse-to-Fine Generation](https://mlsanity.com/paper/2601.08430/) (2026)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [On the Geometry of On-Policy Distillation](https://mlsanity.com/paper/2606.07082/) (2026)
- [Open-MOPD: Diagnosing and Fixing Capability Imbalance in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2608.19098/) (2026)
- [Step-wise Rubric Rewards for LLM Reasoning](https://mlsanity.com/paper/2605.17291/) (2026)
- [One Student, Many Teachers: Multi-Task On-Policy Distillation via Soft-Prompt Privileged Context](https://mlsanity.com/paper/2607.18293/) (2026)
- [When Top-K Misses the Decision: Tool-Call Drift in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2607.07050/) (2026)
- [ConRub-Med: Reinforcement Learning with Consensus Rubrics for Open-Ended Medical Question Answering](https://mlsanity.com/paper/2608.10996/) (2026)

## Abstract (arXiv)

On-policy distillation from multiple teachers combines expertise from different domains in a single student, but conflicting gradients can hinder this integration. Gradient corrections directly constrain parameter updates under plain SGD. With optimizers such as AdamW, however, momentum, adaptive scaling, and weight decay can turn a corrected gradient into an update that increases a domain loss to first order. To address this gap, we propose Update Projection for Multi-Teacher On-Policy Distillation (UP-MOPD). UP-MOPD lets the original mixed gradient update the optimizer state and generate a candidate displacement, then projects only violating candidates before they are committed to the parameters. The projection gives the unique feasible update closest to the candidate in Euclidean distance. In experiments combining medical and general domains, UP-MOPD improves IFEval-loose accuracy late in training by 2.96 points over vanilla M-OPD. It achieves an average score of 60.03 across eight metrics, compared with 59.00 for gradient projection and 59.15 for update rejection. On a public benchmark covering mathematics, code, and instruction following, it achieves the best average across six tasks (32.67), leads on LiveCodeBench v5, and ties for the best IFEval result.These results support projecting optimizer updates to reduce interference between domains.