Papers › LoRA Training in the NTK Regime has No Spurious Local Minima

LoRA Training in the NTK Regime has No Spurious Local Minima

19 Feb 2024arXiv:2402.11867archive 2025-07-28

Uijeong Jang, Jason D. Lee, Ernest K. Ryu

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≲√(N); (ii) using LoRA with rank r≳√(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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