In this paper, we propose a new type of a neural network which is inspired by Gabor systems from harmonic analysis. In this regard, we construct a class of sparsely connected neural networks utilizing the concept of time–frequency shifts, and we show that their approximation error rates can be tied to the number of modulations in the corresponding Gabor frame and to the smoothness of the input function. Furthermore, we show that such networks are easily implementable and we illustrate their performance with some numerical examples.

中文翻译：

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具有证明的逼近性质的Gabor神经网络

在本文中，我们提出了一种新型的神经网络，它受谐波分析的Gabor系统启发。在这方面，我们利用时频偏移的概念构造了一类稀疏连接的神经网络，我们证明了它们的近似误差率可以与相应Gabor帧中的调制次数以及输入的平滑度相关。功能。此外，我们证明了这样的网络很容易实现，并通过一些数值示例说明了它们的性能。