用共享子空间替换LoRA的矩阵B，让微调更高效

In fine-tuning large language models (LLMs), conserving computational resources while maintaining effectiveness and improving outcomes within the same computational constraints is crucial. The Low-Rank Adaptation (LoRA) strategy balances efficiency and performance in fine-tuning large models by reducing the number of trainable parameters and computational costs. However, current advancements in LoRA might be focused on its fine-tuning methodologies, with not as much exploration as might be expected into further compression of LoRA. Since most of LoRA's parameters might still be superfluous, this may lead to unnecessary wastage of computational resources. In this paper, we propose \textbf{CoRA}: leveraging shared knowledge to optimize LoRA training by substituting its matrix $B$ with a common subspace from large models. Our two-fold method includes (1) Freezing the substitute matrix $B$ to halve parameters while training matrix $A$ for specific tasks and (2) Using the substitute matrix $B$ as an enhanced initial state for the original matrix $B$, achieving improved results with the same parameters. Our experiments show that the first approach achieves the same efficacy as the original LoRA fine-tuning while being more efficient than halving parameters. At the same time, the second approach has some improvements compared to LoRA's original fine-tuning performance. They generally attest to the effectiveness of our work.