Fourier neural networks: A comparative study

Zhenisbek Assylbekov, Malika Uteuliyeva, Abylay Zhumekenov, Rustem Takhanov, Alejandro Castro, Olzhas Kabdolov

Abstract: We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them outperforms the standard neural network with sigmoid activation function in the real-world tasks. All neural networks, both Fourier and the standard one, empirically demonstrate lower approximation error than the truncated Fourier series when it comes to approximation of a known function of multiple variables.