LoRA Unleashed: Effortlessly Advancing from Low to Arbitrary Rank

Jiashun Cheng, Aochuan Chen, Ziqi Gao, Yuhan Li, Jia Li, Fugee Tsung

Keywords: low-rank adaptation, parameter-efficient fine-tuning, sparse learning, large language models

Abstract: Low-Rank Adaptation (LoRA) has emerged as a prominent technique for fine-tuning large foundation models, facilitating a reduction in trainable parameters through the utilization of low-rank matrices to represent weight changes $\mathbf{A}$ and $\mathbf{B}$ (\textit{i.e.,} $\Delta \mathbf{W} = \mathbf{B} \mathbf{A}$). Although LoRA has demonstrated considerable success, its expressiveness is inherently limited by the constrained capacity of its low-rank structure. To ameliorate this limitation, we introduce \underline{Fo}urier-based Flexible \underline{R}ank \underline{A}daptation (FoRA), which harnesses the robust expressiveness of the Fourier basis to re-parameterize $\mathbf{A}$ and $\mathbf{B}$ from a sparse spectral subspace. Utilizing FoRA, adaptation matrices can overcome conventional rank limitations, achieving up to a 15x reduction in the parameter budget. We illustrate that FoRA achieves an optimal balance of efficiency and performance across various tasks, including natural language understanding, mathematical reasoning, commonsense reasoning, and image classification. Our codes are available at https://anonymous.4open.science/r/FoRA-0E9C.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 202