Uijeong Jang

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 $r\lesssim \sqrt{N}$; (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.

Chanwoong Park, Uijeong Jang, Ernest K. Ryu et al.

Sharpness-Aware Minimization (SAM) is a widely used method that steers training toward flatter minimizers, which typically generalize better. In this work, however, we show that SAM can converge to hallucinated minimizers -- points that are not minimizers of the original objective. We theoretically prove the existence of such hallucinated minimizers and establish conditions for local convergence to them. We further provide empirical evidence demonstrating that SAM can indeed converge to these points in practice. Finally, we propose a simple yet effective remedy for avoiding hallucinated minimizers.