Spectral Surgery: Training-Free Refinement of LoRA via Gradient-Guided Singular Value Reweighting
Low-Rank Adaptation (LoRA) improves downstream performance by restricting task updates to a low-rank parameter subspace, yet how this limited capacity is allocated within a trained adapter remains unclear. Through a geometric and empirical study across multiple tasks and backbones, we find that trained LoRA updates often exhibit an inefficient spectrum: task effects concentrate in a small subset of singular directions, while many remaining components are neutral or detrimental, motivating post-hoc refinement within the learned subspace. We propose Spectral Surgery, a training-free refinement that decomposes a LoRA update with SVD, estimates per-component sensitivity using gradients on a s...
| Authors | Zailong Tian, Yanzhe Chen, Zhuoheng Han et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 March 2026 |
| Last updated at source | 4 March 2026 |
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