PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer
Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices. These matrices are usually trained with Adam, which treats them as a single flat vector of parameters and ignores both the matrix and product structure of LoRA. Applying a matrix-aware optimizer such as Muon to each factor does not consistently improve over Adam, and neither do the product-aware Muon variants proposed in concurrent works. To realize consistent gains, we introduce PoLoRA, a Preconditioned Orthogonalized LoRA optimizer built from three ingredients: a product-aware spectral update direction, curvat...
| Authors | Nikhil Ghosh, Tetiana Parshakova, Robert M. Gower |
|---|---|
| Primary category | cs.LG |
| Published | 20 July 2026 |
| Last updated at source | 20 July 2026 |
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