用梯度提升思想改进低秩微调，性能接近全量微调但参数少得多

Fine-tuning Large Language Models (LLMs) has become a crucial technique for adapting pre-trained models to downstream tasks. However, the enormous size of LLMs poses significant challenges in terms of computational complexity and resource requirements. Low-Rank Adaptation (LoRA) has emerged as a promising solution. However, there exists a gap between the practical performance of low-rank adaptations and its theoretical optimum. In this work, we propose eXtreme Gradient Boosting LoRA (XGBLoRA), a novel framework that bridges this gap by leveraging the power of ensemble learning. Inspired by gradient boosting, XGBLoRA iteratively learns and merges a sequence of LoRA adaptations to refine model predictions. It achieves better performance than the standard LoRA, while enjoying the computational efficiency of rank-1 adaptations. We provide theoretical analysis to show the convergence and optimality of our approach, and conduct extensive experiments on a range of natural language processing tasks. The results demonstrate that XGBLoRA consistently outperforms standard LoRA and achieves performance comparable to full fine-tuning with significantly fewer trainable parameters. This work advances parameter-efficient fine-tuning for LLMs, and offers a promising solution for adapting LLMs to downstream tasks while optimizing performance and efficiency.