LoRA Training in the NTK Regime has No Spurious Local Minima
<|reference_start|>LoRA Training in the NTK Regime has No Spurious Local Minima: 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.<|reference_end|>
@article{jang2024lora,
    title={LoRA Training in the NTK Regime has No Spurious Local Minima},
    author={Uijeong Jang, Jason D. Lee, Ernest K. Ryu},
    journal={arXiv preprint arXiv:2402.11867},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.11867},
    primaryClass={cs.LG math.OC}
}