Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product $BA$, we observe that the $B$ and $A$ matrices have distinct functions: $A$ extracts features from the input, while $B$ uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning $B$ is inherently more effective than fine-tuning $A$, and that a random untrained $A$ should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training $B$ improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.
@inproceedings{DBLP:conf/icml/ZhuGNBGCGY024,
author = {Jiacheng Zhu and
Kristjan H. Greenewald and
Kimia Nadjahi and
Haitz S{\'{a}}ez de Oc{\'{a}}riz Borde and
Rickard Br{"{u}}el Gabrielsson and
Leshem Choshen and
Marzyeh Ghassemi and
Mikhail Yurochkin and
Justin Solomon},
title = {Asymmetry in Low-Rank Adapters of Foundation Models},
booktitle = {Forty-first International Conference on Machine Learning, {ICML} 2024,
Vienna, Austria, July 21-27, 2024},
publisher = {OpenReview.net},
year = {2024},
url = {https://openreview.net/forum?id=txRZBD8tBV},
timestamp = {Mon, 02 Sep 2024 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/icml/ZhuGNBGCGY024.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
See the full reference list in the paper.