When Is Muon Optimal? Radial Fragility and Minimax Geometry
arXiv:2610.21549v1 Announce Type: cross Abstract: Muon replaces a matrix gradient by an approximate polar factor and has shown strong empirical performance in neural-network training. The Isotropic Curvature Model (ICM) provides a curvature-based explanation for this update by asking when gradient orthogonalization minimizes a one-step local-loss surrogate. We investigate the stability of this explanation when the fixed input radius of the ICM is replaced by a general radial law. We introduce t…