Representations and rates of approximation of real-valued Boolean functions by neural networks

Abstract

We give upper bounds on rates of approximation of real-valued functions of d Boolean variables by one-hidden-layer perceptron networks. Our bounds are of the form c/ n where c depends on certain norms of the function being approximated and n is the number of hidden units. We describe sets of functions where these norms grow either polynomially or exponentially with d.