LoRA-Pro: Are Low-Rank Adapters Properly Optimized?

• URL: http://arxiv.org/abs/2407.18242v2
• Date: Tue, 15 Oct 2024 17:58:24 GMT
• Title: LoRA-Pro: Are Low-Rank Adapters Properly Optimized?
• Authors: Zhengbo Wang, Jian Liang, Ran He, Zilei Wang, Tieniu Tan,
• Abstract summary: Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models. Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning. We introduce LoRA-Pro, a method that enhances LoRA's performance by strategically adjusting the gradients of low-rank matrices.
• Score: 121.0693322732454
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models. Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning. In this paper, we first uncover a fundamental connection between the optimization processes of LoRA and full fine-tuning: using LoRA for optimization is mathematically equivalent to full fine-tuning using a low-rank gradient for parameter updates. And this low-rank gradient can be expressed in terms of the gradients of the two low-rank matrices in LoRA. Leveraging this insight, we introduce LoRA-Pro, a method that enhances LoRA's performance by strategically adjusting the gradients of these low-rank matrices. This adjustment allows the low-rank gradient to more accurately approximate the full fine-tuning gradient, thereby narrowing the performance gap between LoRA and full fine-tuning. Furthermore, we theoretically derive the optimal solutions for adjusting the gradients of the low-rank matrices, applying them during fine-tuning in LoRA-Pro. We conduct extensive experiments across natural language understanding, dialogue generation, mathematical reasoning, code generation, and image classification tasks, demonstrating that LoRA-Pro substantially improves LoRA's performance, effectively narrowing the gap with full fine-tuning. Code is publicly available at \url{https://github.com/mrflogs/LoRA-Pro}.

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