AI RESEARCH
PolarAdamW: Disentangling Spectral Control and Schur Gauge-Equivariance in Matrix Optimisation
arXiv CS.LG
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ArXi:2605.07067v1 Announce Type: new Muon's matrix-level update couples two distinct effects: spectral control via a polar map, and equivariance under orthogonal changes of multiplicity-space basis (Schur gauge-equivariance). We separate them with PolarAdamW, a controlled hybrid that preserves Muon's polar spectral-norm control but breaks the gauge-equivariance, since AdamW's coordinatewise preconditioner is basis-dependent.