Measure Theoretic Results for Approximation by Neural Networks with Limited Weights. (3rd July 2017)

• Record Type: Journal Article
• Authors: Ismailov, Vugar E.; Savas, Ekrem
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 7(2017)
• Page Start: 819
• Page End: 830
• Publication Date: 2017-07-03
• Subjects: Activation function -- Borel measure -- density -- lightning bolt -- neural network -- orthogonal measure -- orbit -- weak convergence; 41A30 -- 41A63 -- 92B20 -- 28A33 -- 46E27; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1254654
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study approximation properties of single hidden layer neural networks with weights varying in finitely many directions and with thresholds from an open interval. We obtain a necessary and simultaneously sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons.