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

arXiv:2610.41104v1 Announce Type: new 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.