fouriermix

**FourierMix** is the **spectral mixing approach that transforms features to frequency domain, applies learnable filtering, and maps back to spatial domain** - by using FFT based global interactions, the model obtains full image receptive field with low computational overhead. **What Is FourierMix?** - **Definition**: A vision block that applies fast Fourier transform to token features, performs spectral modulation, then applies inverse FFT. - **Global Reach**: Every token can influence every other token through frequency coefficients. - **Learnable Spectral Filter**: Model learns which frequencies to amplify or suppress. - **Attention Alternative**: Provides global mixing without explicit pairwise attention matrices. **Why FourierMix Matters** - **Low Cost Global Context**: FFT operations are efficient compared with quadratic attention. - **Frequency Control**: Model can target low frequency semantics and high frequency detail separately. - **Noise Handling**: Unwanted high frequency patterns can be attenuated in spectral space. - **Scalability**: Works well for high resolution images where dense attention is expensive. - **Hybrid Flexibility**: Can be combined with local convolutions or MLP channel mixers. **Spectral Block Components** **FFT Transform**: - Convert spatial feature map into complex frequency coefficients. - Preserve magnitude and phase information. **Learnable Filtering**: - Multiply coefficients by trainable weights or masks. - Controls how each band contributes to reconstruction. **Inverse FFT**: - Return to spatial domain after spectral modulation. - Follow with residual add and normalization. **How It Works** **Step 1**: Compute 2D FFT on feature map or token grid and pass frequency coefficients through learnable spectral filter layers. **Step 2**: Apply inverse FFT, combine with residual path, and continue with task specific head. **Tools & Platforms** - **PyTorch FFT**: Native efficient fft2 and ifft2 APIs. - **CUDA kernels**: Strong acceleration for batched FFT workloads. - **Hybrid backbone repos**: Support plugging spectral blocks into CNN and ViT pipelines. FourierMix is **a fast global mixer that uses spectral math to connect distant regions without quadratic attention cost** - it is especially useful when full context is needed at high resolution.