LoRA Training in the NTK Regime has No Spurious Local Minima

• URL: http://arxiv.org/abs/2402.11867v3
• Date: Tue, 28 May 2024 07:05:05 GMT
• Title: LoRA Training in the NTK Regime has No Spurious Local Minima
• Authors: Uijeong Jang, Jason D. Lee, Ernest K. Ryu,
• Abstract summary: Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models. We theoretically analyze LoRA fine-tuning in the neural tangent kernel regime with $N$ data points.
• Score: 46.46792977614938
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-rank adaptation (LoRA) has become the standard approach for parameter-efficient fine-tuning of large language models (LLM), but our theoretical understanding of LoRA has been limited. In this work, we theoretically analyze LoRA fine-tuning in the neural tangent kernel (NTK) regime with $N$ data points, showing: (i) full fine-tuning (without LoRA) admits a low-rank solution of rank $r\lesssim \sqrt{N}$; (ii) using LoRA with rank $r\gtrsim \sqrt{N}$ eliminates spurious local minima, allowing gradient descent to find the low-rank solutions; (iii) the low-rank solution found using LoRA generalizes well.

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