S^2FT: Parameter-Efficient Fine-Tuning in Sparse Spectrum Domain

Parameter Efficient Fine-Tuning (PEFT) is a key technique for adapting a large pretrained model to downstream tasks by fine-tuning only a small number of parameters. Recent methods based on Fourier transforms have further reduced the fine-tuned parameters scale by only fine-tuning a few spectral coefficients. Its basic assumption is that the weight change $\Delta W$ is a spatial-domain matrix with a sparse spectrum. However, in this paper, we observe that the spectrum of weight change is not sparse, but instead distributed like power-uniform. This fact implies that fine-tuning only a few spectral coefficients is insufficient to accurately model the weight change $\Delta W$ with uniform spectrum.To address this issue, we propose to seek an invertible transformation that can transform a latent spatial-domain matrix with sparse spectrum to the weight change, and then perform PEFT on such sparse spectrum domain with few spectral coefficients, called $\text{S}^2\text{FT}$. To seek such transformation, we first pre-estimate a coarse weight change as a prior. Then, inspired by that sparse spectrum often correspond to locally smooth spatial structures, we regard this transformation as a row and column rearrangement operation on the pre-estimated weight change that smooth spatial structures while keep the structure information of neurons.Finally, we propose to solve the rearrangement search problem in a simple nearest neighbor search manner, thereby obtaining the invertible transformation. Extensive results show our $\text{S}^2\text{FT}$ achieves superior performance by only using 0.08% training parameters.