Training-Loss Guarantees for Muon with Finite-Step Newton--Schulz Orthogonalization

arXiv:2610.03306v1 Announce Type: cross Abstract: Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton--Schulz polynomials, and guarantee only stationarity, so it is unresolved what Muon's five tuned Newton--Schulz steps preserve and whether that suffices to reach a prescribed neural-network training loss. We establish a finite-time training guarantee that accounts for both momentum accumulation before orthogonalization and the tuned finite-step update. For full-batch training of a sufficiently wide two-layer ReLU network with fixed random out

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