MALT: Lightweight Curvature-Aware Muon via Diagonal Preconditioning
Muon has recently emerged as a promising alternative to AdamW for language model pretraining by orthogonalizing momentum matrices using Newton-Schulz iterations. Although Muon mitigates gradient anisotropy, it does not explicitly account for the curvature geometry of the loss landscape and may therefore remain sensitive to curvature anisotropy. We bridge this gap by proposing MALT (Muon Augmented by Lightweight Two-sided Preconditioning), which uses lightweight diagonal preconditioners to reduce the sensitivity of Muon to curvature anisotropy. Specifically, MALT uses two-sided diagonal preconditioners with low memory and computational overhead to approximately capture the curvature geomet...
| Authors | Tongle Wu, Huanyu Dong, Ying Sun et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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