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.

翻译：本文研究了一类新的径向基函数（RBF）神经网络，其中平滑因子被替换为平移量。我们证明，在激活函数满足特定条件的情况下，此类网络能够逼近$d$维欧氏空间任意紧子集上的任意连续多元函数。针对具有有限固定中心的RBF网络，我们给出了确保任意精度逼近的条件。