arXiv — cs.AI preprintsInternational9 October 2026
From Geometry to Generalization: Why Row Normalization Can Beat Adam and Muon
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arXiv:2610.11309v1 Announce Type: cross Abstract: Different optimizers can fit the same training data while selecting classifiers with substantially different geometries, but whether this difference provably affects population performance remains unclear. We show that row-wise normalization can achieve strictly higher population accuracy than full-batch Adam, a proxy for random-reshuffling Adam, and exact-SVD Muon in high-dimensional multiclass classification. Under an isotropic Gaussian-cloud data model, this advantage arises because row normalization's class-wise Euclidean geometry asymptoti
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