LoRA-Muon: New Optimizer Improves Low-Rank Adaptation for Fine-Tuning Deep Learning Models
Researchers have proposed LoRA-Muon, an optimizer that applies the Muon optimizer's spectral steepest-descent rule to Low-Rank Adaptation (LoRA) finetuning of deep learning models. LoRA is widely used to reduce compute and memory costs but has historically been difficult to tune, with learning rates that transfer poorly across different rank settings. The work claims LoRA-Muon resolves these issues, achieving learning rate transferability across rank, width, and depth, and outperforming dense baselines in controlled experiments.
Low-Rank Adaptation (LoRA) is a popular technique for finetuning large deep learning models at reduced computational and memory cost, but it has long suffered from sensitivity to initialization and poor learning rate transferability across ranks compared to dense training. The new preprint, submitted to arXiv on June 11, 2026, introduces LoRA-Muon, derived by applying the Muon optimizer's spectral steepest-descent update rule to the low-rank manifold, paired with a novel split weight-decay rule. The authors argue that LoRA-Muon serves as a strong low-rank proxy for full-rank Muon and Shampoo-family optimizers, with optimal learning rates that transfer across rank, width, depth, and factor rescaling. In compute-matched experiments on TinyShakespeare, a rank-2 LoRA-Muon proxy recovered the dense model's best tested learning rate, and a rank-32 run achieved lower mean validation loss than the dense baseline in a seed-averaged sweep. The paper also critiques competing approaches: it argues the Spectron optimizer is sensitive to arbitrary factor scaling and would likely perform poorly when finetuning from imbalanced factors, and it shows that LoRA-RITE's core implements the same spectral update as LoRA-Muon but requires QR-decomposition and second-moment storage, making LoRA-Muon more memory-efficient and accelerator-friendly.
What's missing
The study's own limitations include reliance on a small-scale benchmark (TinyShakespeare), leaving open whether results generalize to large-scale language model finetuning tasks. The paper has not yet undergone peer review, as it is a preprint.
What different sources said
- arXiv cs.AICenter
LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold
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