DiffoRA: Enabling Parameter-Efficient LLM Fine-Tuning via Differential Low-Rank Matrix Adaptation

The Parameter-Efficient Fine-Tuning (PEFT) methods have been extensively researched for large language models in the downstream tasks. Among all the existing approaches, the Low-Rank Adaptation (LoRA) has gained popularity for its streamlined design by incorporating low-rank matrices into existing pre-trained models. Though effective, LoRA allocates every module an identical low-rank matrix, which ignores the varying properties and contributions across different components. Moreover, the existing adaptive LoRA solutions rely highly on intuitive importance scoring indicators to adjust the interior rank of the decomposition matrices. In this paper, we propose a new PEFT scheme called DiffoRA, which is theoretically grounded and enables module-wise adoption of LoRA. At the core of our DiffoRA lies a Differential Adaptation Matrix (DAM) to determine which module is the most suitable and essential for fine-tuning. We explain how the designed matrix impacts the convergence rate and generalization capability of a pre-trained model. Furthermore, we construct the DAM via continuous relaxation and discretization with weight-sharing optimizations. We fully implement our DiffoRA and design comprehensive experiments to evaluate its performance. The experimental results demonstrate that our approach achieves the best model accuracy over all the state-of-the-art baselines across various benchmarks.