title: Multivariate neural network operators with sigmoidal activation functions.
abstract: In this paper, we study pointwise and uniform convergence, as well as order of approximation, of a family of linear positive multivariate neural network (NN) operators with sigmoidal activation functions. The order of approximation is studied for functions belonging to suitable Lipschitz classes and using a moment-type approach. The special cases of NN operators, activated by logistic, hyperbolic tangent, and ramp sigmoidal functions are considered. Multivariate NNs approximation finds applications, typically, in neurocomputing processes. Our approach to NN operators allows us to extend previous convergence results and, in some cases, to improve the order of approximation. The case of multivariate quasi-interpolation operators constructed with sigmoidal functions is also considered.
authors: Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre", 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy. Electronic address: costarel@mat.uniroma3.it.
authors: Danilo
authors: D
authors: Costarelli
authors: Renato
authors: R
authors: Spigler
mesh_terms: D000465:Algorithms; D003205:Computing Methodologies; D016014:Linear Models; D015999:Multivariate Analysis; D016571:Neural Networks, Computer; D011382:Programming, Linear
keywords: Lipschitz classes; Multivariate neural networks operators; Order of approximation; Sigmoidal functions; Uniform approximation