On the Kolmogorov neural networks

In this paper, we show that the Kolmogorov two hidden layer neural network model with a continuous, discontinuous bounded or unbounded activation function in the second hidden layer can precisely represent continuous, discontinuous bounded and all unbounded multivariate functions, respectively.

On the universal approximation property of radial basis function neural networks

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.