AI RESEARCH
Phases of Muon: When Muon Eclipses SignSGD
arXiv CS.LG
•
ArXi:2605.09552v1 Announce Type: cross Recently, Muon and related spectral optimizers have nstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behaviour remains poorly understood. We analyze stochastic spectral optimizers, including Muon, on a high-dimensional matrix-valued least squares problem. We derive explicit deterministic dynamics that provide a tractable framework for studying learning behaviour with a focus on (stochastic) SignSVD, which Muon approximates, and (stochastic) SignSGD, the latter serving as a proxy for Adam.