In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the d-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.

中文翻译：

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径向基函数神经网络的万能逼近性质

在本文中，我们考虑一类新的 RBF（径向基函数）神经网络，其中平滑因子被移位取代。我们证明在激活函数的某些条件下，这些网络能够逼近d维欧几里德空间的任何紧凑子集上的任何连续多元函数。对于具有有限多个固定质心的 RBF 网络，我们描述了保证任意精度近似的条件。