A Note on the Convergence of Muon

Jiaxiang Li; Mingyi Hong

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arXiv · 2502.02900

A Note on the Convergence of Muon

Jiaxiang Li·Mingyi Hong

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Abstract

In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent method where the update direction is the minimizer of the quadratic approximation of the objective function under spectral norm. We provide the convergence analysis on both versions of the optimizer and discuss its implications.

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Jiaxiang Li, Mingyi Hong. 2025-02-05. A Note on the Convergence of Muon. https://arxiv.org/abs/2502.02900

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