Parameter-Efficient Fine-Tuning with Discrete Fourier Transform

Ziqi Gao, Qichao Wang, Aochuan Chen, Zijing Liu, Bingzhe Wu, Liang Chen, Jia Li
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:14884-14901, 2024.

Abstract

Low-rank adaptation (LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices $A$ and $B$ to represent the weight change, i.e., $\Delta W=BA$. Despite LoRA’s progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats $\Delta W$ as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover $\Delta W$. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA’s 33.5M. Our code is released at this link.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-gao24o, title = {Parameter-Efficient Fine-Tuning with Discrete {F}ourier Transform}, author = {Gao, Ziqi and Wang, Qichao and Chen, Aochuan and Liu, Zijing and Wu, Bingzhe and Chen, Liang and Li, Jia}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {14884--14901}, 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/gao24o/gao24o.pdf}, url = {https://proceedings.mlr.press/v235/gao24o.html}, abstract = {Low-rank adaptation (LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices $A$ and $B$ to represent the weight change, i.e., $\Delta W=BA$. Despite LoRA’s progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats $\Delta W$ as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover $\Delta W$. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA’s 33.5M. Our code is released at this link.} }
Endnote
%0 Conference Paper %T Parameter-Efficient Fine-Tuning with Discrete Fourier Transform %A Ziqi Gao %A Qichao Wang %A Aochuan Chen %A Zijing Liu %A Bingzhe Wu %A Liang Chen %A Jia Li %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-gao24o %I PMLR %P 14884--14901 %U https://proceedings.mlr.press/v235/gao24o.html %V 235 %X Low-rank adaptation (LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices $A$ and $B$ to represent the weight change, i.e., $\Delta W=BA$. Despite LoRA’s progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats $\Delta W$ as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover $\Delta W$. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA’s 33.5M. Our code is released at this link.
APA
Gao, Z., Wang, Q., Chen, A., Liu, Z., Wu, B., Chen, L. & Li, J.. (2024). Parameter-Efficient Fine-Tuning with Discrete Fourier Transform. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:14884-14901 Available from https://proceedings.mlr.press/v235/gao24o.html.

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