title: Universal approximation by radial basis function networks of Delsarte translates.
abstract: We prove that, under certain mild conditions on the kernel function (or activation function), the family of radial basis function neural networks obtained by replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, has the universal approximation property.
authors.affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain. cclement@ull.es
authors.forename: Cristian
authors.initials: C
authors.lastname: Arteaga
authors.forename: Isabel
authors.initials: I
authors.lastname: Marrero
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D013223:Statistics as Topic
keywords: Activation function; Bessel convolution; Delsarte translation operator; Density; Radial basis function network; Universal approximation