Dimension-independent bounds on the degree of approximation by neural networks
by H. N. Mhaskar, C. A. Micchelli
Let ɸ be a univariate 2π-periodic function. Suppose that s ≥ 1 and f is a 2π-periodic function of s real variables. We study sufficient conditions in order that a neural network having a single hidden layer consisting of n neurons, each with an activation function ɸ, can be constructed so as to give a mean square approximation to f within a given accuracy ϵn, independent of the number of variables. We also discuss the case in which the activation function ɸ is not 2π-periodic.