Muon is Not That Special: Random or Inverted Spectra Work Just as Well

ArXi:2605.11181v1 Announce Type: cross The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear minimization oracle (LMO) theory. In this paper, we challenge this geometric narrative through three contributions, nstrating that precise geometric structure is not the key factor affecting optimization performance. First, we