Saturation Classes for Max-Product Neural Network Operators Activated by Sigmoidal Functions

Abstract

In the present paper, we obtain a saturation result for the neural network (NN) operators of the max-product type. In particular, we show that any non-constant, continuous function on the interval [0, 1] cannot be approximated by the above operators $$F^{(M)}_n$$ , $$n \in \mathbb {N}^+$$ , by a rate of convergence higher than 1 / n. Moreover, since we know that any Lipschitz function f can be approximated by the NN operators with an order of approximation of 1 / n, here we are able to prove a local inverse result, in order to provide a characterization of the saturation (Favard) classes.