title: Essential rate for approximation by spherical neural networks.
abstract: We consider the optimal rate of approximation by single hidden feed-forward neural networks on the unit sphere. It is proved that there exists a neural network with n neurons, and an analytic, strictly increasing, sigmoidal activation function such that the deviation of a Sobolev class W²(2r)(S(d)) from the class of neural networks Φ(n)(ϕ), behaves asymptotically as n(-2r/d-1). Namely, we prove that the essential rate of approximation by spherical neural networks is n(-2r/d-1).
authors.affiliation: Institute for Information and System Sciences, Xi'an Jiaotong University, Xi'an 710049, Shannxi Province, PR China. ssxvkihc@yahoo.com.cn
authors.forename: Shaobo
authors.initials: S
authors.lastname: Lin
authors.forename: Feilong
authors.initials: F
authors.lastname: Cao
authors.forename: Zongben
authors.initials: Z
authors.lastname: Xu
mesh_terms: D000465:Algorithms; D006801:Humans; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*