LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for
  Parameter-Efficient Fine-Tuning
Authors: name: Yiming Shi, name: Jiwei Wei, name: Yujia Wu, name: Ran Ran, name: Chengwei Sun, name: Shiyuan He, name: Yang Yang

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. 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. To
address these issues, we propose 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 Decomposition (LDU) to initialize low-rank
matrices for faster convergence and orthogonality. 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, 6 natural
language understanding (NLU) datasets, 8 image classification datasets, and
image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and
Stable Diffusion), providing a comprehensive and detailed analysis. Our
open-source code can be accessed at
https://github.com/SKDDJ/LoLDU{https://github.com/SKDDJ/LoLDU}.