Asymmetry in Low-Rank Adapters of Foundation Models
<|reference_start|>Asymmetry in Low-Rank Adapters of Foundation Models: 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.<|reference_end|>
@article{zhu2024asymmetry,
    title={Asymmetry in Low-Rank Adapters of Foundation Models},
    author={Jiacheng Zhu, Kristjan Greenewald, Kimia Nadjahi, Haitz S'aez de
  Oc'ariz Borde, Rickard Br"uel Gabrielsson, Leshem Choshen, Marzyeh
  Ghassemi, Mikhail Yurochkin, Justin Solomon},
    journal={arXiv preprint arXiv:2402.16842},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.16842},
    primaryClass={cs.LG}
}