Fourier Neural Networks: A Comparative Study
This work provides an empirical evaluation of Fourier neural networks, showing they are incremental and do not offer advantages over existing methods in practical scenarios.
The paper compared Fourier neural networks to standard neural networks on synthetic and real-world tasks, finding that Fourier networks did not outperform standard networks in real-world applications, and all networks had lower approximation errors than truncated Fourier series for multi-variable functions.
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 an approximation of a known function of multiple variables.