Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering

arXiv:2606.03899v1 Announce Type: new Abstract: Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, the

Source: arXiv cs.LG — read the full report at the original publisher.

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