MUON-RT Reusing the Teacher's Trajectory for Momentum-Free Muon for LLM Self-Distillation
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.
Related
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BibTeX
@misc{das2026muonrt,
title = {{MUON-RT Reusing the Teacher's Trajectory for Momentum-Free Muon for LLM Self-Distillation}},
author = {Aryan Das and Vinay Kumar Verma and Aakansha Mishra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41104},
eprint = {2610.41104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41104},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - MUON-RT Reusing the Teacher's Trajectory for Momentum-Free Muon for LLM Self-Distillation
AU - Aryan Das
AU - Vinay Kumar Verma
AU - Aakansha Mishra
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41104
UR - https://arxiv.org/abs/2610.41104
AB - 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.
ER -