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 , , 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.

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

Costarelli, Danilo;Vinti, Gianluca
2017

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 , , 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.
2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1422068
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