LoRA-One: One-Step Full Gradient Could Suffice for Fine-Tuning Large Language Models, Provably and Efficiently

• URL: http://arxiv.org/abs/2502.01235v3
• Date: Mon, 23 Jun 2025 09:29:57 GMT
• Title: LoRA-One: One-Step Full Gradient Could Suffice for Fine-Tuning Large Language Models, Provably and Efficiently
• Authors: Yuanhe Zhang, Fanghui Liu, Yudong Chen,
• Abstract summary: This paper explores how theory can guide and enhance practical algorithms, using Low-Rank Adaptation (LoRA) in large language models.<n>We rigorously prove that, under gradient descent, LoRA adapters align with specific singular subspaces of the one-step full fine-tuning gradient.<n>We propose a theory-driven algorithm, LoRA-One, where the linear convergence is built and incorporating preconditioners helps mitigate the effects of ill-conditioning.
• Score: 10.843508549704959
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper explores how theory can guide and enhance practical algorithms, using Low-Rank Adaptation (LoRA, Hu et al. 2022) in large language models as a case study. We rigorously prove that, under gradient descent, LoRA adapters align with specific singular subspaces of the one-step full fine-tuning gradient. This result suggests that, by properly initializing the adapters using the one-step full gradient, subspace alignment can be achieved immediately and applicable to both linear and nonlinear models. Building on our theory, we propose a theory-driven algorithm, LoRA-One, where the linear convergence (as well as generalization) is built and incorporating preconditioners theoretically helps mitigate the effects of ill-conditioning. Besides, our theory reveals connections between LoRA-One and other gradient-alignment-based methods, helping to clarify misconceptions in the design of such algorithms. LoRA-One achieves significant empirical improvements over LoRA and its variants across benchmarks in natural language understanding, mathematical reasoning, and code generation. Code is available at: https://github.com/YuanheZ/LoRA-One.

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