Approximation of functions by perceptrons: a new approach

摘要

We provide a constructive proof of the theorem of function approximation by perceptrons (cf Leshno et al. [1], Hornik [2]) when the activation function ψ isC∞ with all its derivatives non 0 at 0. We deal with uniform approximation on compact sets of continuous functions on ℜd,d≥1. This approach is elementary and provides some approximation results for the derivatives along with some bounds for the hidden layer.