Fouriertransformer

Fouriertransformer is a neural network architecture that integrates Fourier analysis with the Transformer framework to model sequential and structured data. By projecting inputs into the frequency domain via the discrete Fourier transform, the model can mix information across distant elements and capture global patterns that are difficult for conventional time-domain attention to learn. This spectral perspective can improve modeling of smooth, long-range dependencies while enabling new forms of data interaction.

Typical designs apply the fast Fourier transform to input sequences or feature maps, perform a learned spectral operation in frequency space, and then transform back with the inverse FFT. Some variants combine spectral mixing with standard time-domain self-attention, or use localized Fourier windows to balance global and local information. The approach can reduce computational complexity by operating on a reduced set of frequency components or by leveraging efficient FFT implementations.

Mathematically, Fouriertransformers rely on the convolution theorem and, in many implementations, complex-valued representations. They enable global mixing through frequency components and can exploit linear or near-linear scaling with sequence length under certain conditions. They may emphasize smooth, coherent structures but can require careful handling of boundary conditions and high-frequency details that appear in non-stationary data.

Applications span natural language processing, time-series forecasting, audio and speech processing, image and video modeling, and scientific computing tasks involving structured signals. The Fouriertransformer is part of a broader movement toward spectral or frequency-domain neural models that complement traditional time-domain attention.

See also: Transformer, Fourier transform, spectral attention, Fourier neural operator.