Approximation of functions by perceptrons: a new approach

Abstract

Abstract. We provide a constructive proof of the theorem of function approximation by perceptrons (of Leshno et al. [i], Homik [2] ) when the activation function W is C" with all its derivatives non 0 at 0. We deal with uniform approximation on compact sets of continuous functions on 91 a, d> 1. This approach is elementary and provides some approximation results for the derivatives along with some bounds for the hidden layer.