Dimension-independent bounds on the degree of approximation by neural networks
Hrushikesh N. Mhaskar, Charles A. Micchelli · IBM Journal of Research and Development · 1994
Let φ 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 φ, can be constructed so as to give a mean square approximation to f within a given accuracy ∈n, independent of the number of variables. We also discuss the case in which the activation function φ is not 2π-periodic.