SBoRA: Low-Rank Adaptation with Regional Weight Updates

Abstract: This paper introduces Standard Basis LoRA (SBoRA), a novel parameter-efficient fine-tuning approach for LLMs that builds upon the pioneering works of Low-Rank Adaptation (LoRA) and Orthogonal Adaptation. SBoRA reduces the number of trainable parameters by half or doubles the rank with the similar number of trainable parameters as LoRA, while improving learning performance. By utilizing orthogonal standard basis vectors to initialize one of the low-rank matrices (either $\mathbf{A}$ or $\mathbf{B}$), SBoRA facilitates regional weight updates and memory-efficient fine-tuning. This results in two variants, SBoRA-FA and SBoRA-FB, where only one of the matrices is updated, leading to a sparse update matrix $\mathrm{\Delta} \mathbf{W}$ with predominantly zero rows or columns. Consequently, most of the fine-tuned model's weights $(\mathbf{W}_0+\mathrm{\Delta} \mathbf{W})$ remain unchanged from the pre-trained weights, akin to the modular organization of the human brain, which efficiently adapts to new tasks. Our empirical results demonstrate the superiority of SBoRA-FA over LoRA in various fine-tuning tasks, including commonsense reasoning and arithmetic reasoning. Furthermore, we evaluate the effectiveness of QSBoRA on quantized LLaMA models of varying scales, highlighting its potential for efficient adaptation to new tasks. Code is available at https://github.com/cityuhkai/SBoRA