Parameter-Efficient Fine-Tuning with Discrete Fourier Transform
This addresses storage efficiency for researchers and practitioners fine-tuning large foundation models, offering an incremental improvement over existing parameter-efficient methods.
The paper tackles the storage challenge in fine-tuning large models by introducing FourierFT, a method that compresses trainable parameters using the Fourier transform, achieving comparable or better performance with significantly fewer parameters, such as surpassing LoRA on LLaMA2-7B with only 0.064M parameters versus 33.5M.
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., $ΔW=BA$. 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 $ΔW$ 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 $ΔW$. 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 \url{https://github.com/Chaos96/fourierft}.