LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for Parameter-Efficient Fine-Tuning

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as low-rank adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning (FT). However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning (FT). To address these issues, we propose low-rank LDU (LoLDU), a parameter-efficient fine-tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages lower-diag-upper (LDU) decomposition to initialize low-rank matrices for faster convergence and nonsingularity. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, six natural language understanding (NLU) datasets, eight image classification datasets, and image generation datasets with multiple model types [LLaMA2, RoBERTa, ViT, and stable diffusion (SD)], providing a comprehensive and detailed analysis. Our open-source code can be accessed at https://anonymous.4open.science/r/LoLDU-B5A6.