Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization
Authors: name: Weiyang Liu, name: Zeju Qiu, name: Yao Feng, name: Yuliang Xiu, name: Yuxuan Xue, name: Longhui Yu, name: Haiwen Feng, name: Zhen Liu, name: Juyeon Heo, name: Songyou Peng, name: Yandong Wen, name: Michael J. Black, name: Adrian Weller, name: Bernhard Schölkopf

Large foundation models are becoming ubiquitous, but training them from
scratch is prohibitively expensive. Thus, efficiently adapting these powerful
models to downstream tasks is increasingly important. In this paper, we study a
principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream
task adaptation. Despite demonstrating good generalizability, OFT still uses a
fairly large number of trainable parameters due to the high dimensionality of
orthogonal matrices. To address this, we start by examining OFT from an
information transmission perspective, and then identify a few key desiderata
that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast
Fourier transform algorithm enables efficient information transmission, we
propose an efficient orthogonal parameterization using butterfly structures. We
apply this parameterization to OFT, creating a novel parameter-efficient
finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a
special case, BOFT introduces a generalized orthogonal finetuning framework.
Finally, we conduct an extensive empirical study of adapting large vision
transformers, large language models, and text-to-image diffusion models to
various downstream tasks in vision and language.