Neural Networks for Approximation of Real Functions with the Gaussian Functions

We present a type of single-hidden layer feedforward neural networks with the Gaussian activation function. First, we give a new and quantitative proof of the fact that a single layer neural networks with n + 1 hidden neurons can learn n + 1 distinct samples with zero error. Then we give approximate interpolants. They can approximate interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. They can uniformly approximate any continuous function of one variable.