# MUON-RT Reusing the Teacher's Trajectory for Momentum-Free Muon for LLM Self-Distillation

**Authors:** Aryan Das, Vinay Kumar Verma, Aakansha Mishra  
**Lab:** Indian Institute of Technology, Kanpur · **Published:** 29 Oct 2026 · **Upvotes:** 14  
**Links:** [arXiv](https://arxiv.org/abs/2610.41104) · [PDF](https://arxiv.org/pdf/2610.41104) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2610.41104.html)

## Key numbers

- **42%**: Muon-RT improves average accuracy over AdamW by 2.6 points with 42% less persistent memory
- **27%**: and over momentum Muon by 5.4 points with 27% less persistent memory

## Abstract

Self-distillation methods for large language models with an exponential moving average (EMA) teacher already retain a history of student updates. Muon nevertheless stores a separate momentum buffer, increasing persistent training memory. We propose Muon with Reused Teacher (Muon-RT), which reuses the teacher-student displacement to eliminate momentum buffers for hidden weight matrices. We show that this displacement encodes an exponentially weighted history of applied updates and smooths temporally uncorrelated noise under a local model. Muon-RT removes its radial component, normalizes it spectrally, and mixes it with the current gradient after Newton-Schulz (NS) orthogonalization. Under explicit regularity and alignment assumptions, we establish linear contraction of an expected objective-gap bound toward a residual error level. With Self-Distillation Fine-Tuning (SDFT) on Qwen2.5-7B-Instruct, Muon-RT improves average accuracy over AdamW by 2.6 points with 42% less persistent memory, and over momentum Muon by 5.4 points with 27% less persistent memory. With Self-Distillation Policy Optimization (SDPO) on Olmo-3-7B-Instruct, it improves average accuracy over AdamW by 2.0 points.

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