This paper introduces FourierFT (Fourier Transform for Fine-Tuning), a parameter-efficient fine-tuning method for large foundation models (LFMs). FourierFT leverages the Fourier transform to compress the weight changes $\Delta W$ by learning only a small fraction of its spectral coefficients, significantly reducing the number of trainable parameters. Unlike LoRA, which uses low-rank matrices, FourierFT treats $\Delta W$ as a spatial domain matrix and learns sparse spectral coefficients. The method is evaluated on various tasks, including natural language understanding, generation, instruction tuning, and image classification. Empirical results show that FourierFT achieves comparable or better performance with significantly fewer parameters compared to LoRA. For example, on the LLaMA2-7B model, FourierFT outperforms LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. The code for FourierFT is available at <https://github.com/Chaos96/fourierft>.This paper introduces FourierFT (Fourier Transform for Fine-Tuning), a parameter-efficient fine-tuning method for large foundation models (LFMs). FourierFT leverages the Fourier transform to compress the weight changes $\Delta W$ by learning only a small fraction of its spectral coefficients, significantly reducing the number of trainable parameters. Unlike LoRA, which uses low-rank matrices, FourierFT treats $\Delta W$ as a spatial domain matrix and learns sparse spectral coefficients. The method is evaluated on various tasks, including natural language understanding, generation, instruction tuning, and image classification. Empirical results show that FourierFT achieves comparable or better performance with significantly fewer parameters compared to LoRA. For example, on the LLaMA2-7B model, FourierFT outperforms LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. The code for FourierFT is available at <https://github.com/Chaos96/fourierft>.