This paper introduces FourierFT, a parameter-efficient fine-tuning method that leverages the discrete Fourier transform (DFT) to reduce the number of trainable parameters in large foundation models (LFMs). Unlike LoRA, which uses low-rank matrices to approximate weight changes, FourierFT treats the weight change as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. By applying the inverse discrete Fourier transform (IDFT) to these coefficients, FourierFT recovers the weight change without explicitly storing the full matrix. This approach significantly reduces the number of trainable parameters while maintaining performance comparable to or better than LoRA on various tasks, including natural language understanding, generation, instruction tuning, and image classification. The method works by randomly selecting a subset of spectral entries and learning only the coefficients at these entries. These coefficients are then used to compute the weight change through IDFT. FourierFT is implemented with a parameter-efficient design that allows it to store only a small number of parameters, making it suitable for deployment on resource-constrained systems. The method is evaluated on multiple tasks, including the GLUE benchmark for NLP and image classification tasks, demonstrating its effectiveness in reducing parameter count while maintaining high performance. Compared to LoRA, FourierFT achieves a significant reduction in the number of trainable parameters, with results showing that it can outperform LoRA on several tasks with fewer parameters. For example, on instruction tuning, FourierFT with 64K trainable parameters outperforms LoRA with 33.5M parameters. The method is also shown to be effective in image classification tasks, achieving performance comparable to full fine-tuning with significantly fewer parameters. The paper also explores the impact of frequency bias on performance, showing that FourierFT can achieve strong results even without any frequency bias. Additionally, the method is shown to be scalable, with performance improving as the number of parameters increases. The results demonstrate that FourierFT is a promising approach for parameter-efficient fine-tuning of large foundation models, offering a balance between performance and computational efficiency.This paper introduces FourierFT, a parameter-efficient fine-tuning method that leverages the discrete Fourier transform (DFT) to reduce the number of trainable parameters in large foundation models (LFMs). Unlike LoRA, which uses low-rank matrices to approximate weight changes, FourierFT treats the weight change as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. By applying the inverse discrete Fourier transform (IDFT) to these coefficients, FourierFT recovers the weight change without explicitly storing the full matrix. This approach significantly reduces the number of trainable parameters while maintaining performance comparable to or better than LoRA on various tasks, including natural language understanding, generation, instruction tuning, and image classification. The method works by randomly selecting a subset of spectral entries and learning only the coefficients at these entries. These coefficients are then used to compute the weight change through IDFT. FourierFT is implemented with a parameter-efficient design that allows it to store only a small number of parameters, making it suitable for deployment on resource-constrained systems. The method is evaluated on multiple tasks, including the GLUE benchmark for NLP and image classification tasks, demonstrating its effectiveness in reducing parameter count while maintaining high performance. Compared to LoRA, FourierFT achieves a significant reduction in the number of trainable parameters, with results showing that it can outperform LoRA on several tasks with fewer parameters. For example, on instruction tuning, FourierFT with 64K trainable parameters outperforms LoRA with 33.5M parameters. The method is also shown to be effective in image classification tasks, achieving performance comparable to full fine-tuning with significantly fewer parameters. The paper also explores the impact of frequency bias on performance, showing that FourierFT can achieve strong results even without any frequency bias. Additionally, the method is shown to be scalable, with performance improving as the number of parameters increases. The results demonstrate that FourierFT is a promising approach for parameter-efficient fine-tuning of large foundation models, offering a balance between performance and computational efficiency.