Convergence of Practical Muon
Muon is emerging as a promising alternative to AdamW for large-scale neural network training, yet theoretical understanding of its practical implementation remains incomplete, as existing analyses often simplify or omit two key components: (i) practical Newton--Schulz iterations with empirically tuned polynomial coefficients $(3.4445,-4.7750,2.0315)$; and (ii) decoupled weight decay for regularization. In this paper, we provide an optimization interpretation and establish convergence for practical Muon, jointly accounting for both components. Specifically, we interpret practical Muon as right-preconditioned optimization of the original loss with a dynamic weighted $\ell_2$ regularizer tha...
| Authors | Haonan Wang, Yu Wu, Minghui Liwang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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