Reassessing Muon for Matrix Factorization
Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training. Its empirical success has motivated a growing body of theoretical work that interprets Muon as steepest descent under the spectral norm. Yet it remains unclear which of Muon's advantages stem from its update rule itself and which are artifacts of the scale, architecture, and data of modern deep networks. In this work, we isolate the optimizer from these confounding factors by studying Muon on a simple, well-understood, and spectrally structured problem: lo...
| Authors | Ali Parviz, Gal Mishne, Alex Cloninger |
|---|---|
| Primary category | cs.LG |
| Published | 14 July 2026 |
| Last updated at source | 1 August 2026 |
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