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arXiv Machine Learning By Mingyi Li, Taira Tsuchiya

Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization

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The paper introduces Muon, an optimizer that uses a finite number of Newton‑Schulz iterations to approximate the polar factor for matrix‑valued parameters in large language model pretraining. It demonstrates that this finite iteration smooths the discontinuous polar map into a Lipschitz function of singular values, enabling a conversion from online learning regret to a stationarity guarantee in nonsmooth nonconvex optimization. The authors prove that a logarithmic depth in Newton‑Schulz suffices for convergence to stationary points, matching best‑known sample complexity bounds and extending the result to other spectral maps with similar smoothing properties.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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