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arXiv · 2402.11867

LoRA Training in the NTK Regime has No Spurious Local Minima

Uijeong Jang·Jason D. Lee·Ernest K. Ryu
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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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Uijeong Jang, Jason D. Lee, Ernest K. Ryu. 2024-02-19. LoRA Training in the NTK Regime has No Spurious Local Minima. https://arxiv.org/abs/2402.11867

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