LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold
Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines. We derive LoRA-Muon by applying the Muon optimizer's spectral steepest-descent rule to the low-rank setting. Along with our split weight-decay rule, our main claim is that LoRA-Muon is a good low-rank proxy for full-rank Muon and Shampoo-family optimizers. Its optimal learning rates transfer across rank, width, depth, and factor-rescaling. In ...
| Authors | Franz Louis Cesista, Katherine Crowson, Cédric Simal et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 June 2026 |
| Last updated at source | 11 June 2026 |
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