LoRA Training in the NTK Regime has No Spurious Local Minima

Uijeong Jang, Jason D. Lee, Ernest K. Ryu
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:21306-21328, 2024.

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≲; (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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-jang24d, title = {{L}o{RA} Training in the {NTK} Regime has No Spurious Local Minima}, author = {Jang, Uijeong and Lee, Jason D. and Ryu, Ernest K.}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {21306--21328}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/jang24d/jang24d.pdf}, url = {https://proceedings.mlr.press/v235/jang24d.html}, 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.} }
Endnote
%0 Conference Paper %T LoRA Training in the NTK Regime has No Spurious Local Minima %A Uijeong Jang %A Jason D. Lee %A Ernest K. Ryu %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-jang24d %I PMLR %P 21306--21328 %U https://proceedings.mlr.press/v235/jang24d.html %V 235 %X 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.
APA
Jang, U., Lee, J.D. & Ryu, E.K.. (2024). LoRA Training in the NTK Regime has No Spurious Local Minima. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:21306-21328 Available from https://proceedings.mlr.press/v235/jang24d.html.

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