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.

中文翻译：

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傅立叶神经网络：一项比较研究

我们回顾了以傅立叶级数和积分为动力的神经网络架构，这些架构被称为傅立叶神经网络。这些网络在合成任务和实际任务中都经过经验评估。在现实世界中的任务中，它们都不能超过具有S型激活功能的标准神经网络。在对多个变量的已知函数进行逼近时，所有神经网络（无论是傅立叶还是标准神经网络）在经验上均比截断的傅立叶级数具有更低的逼近误差。