Measure Theoretic Results for Approximation by Neural Networks with Limited Weights

Ismailov V. E., Savas E.

Numerical Functional Analysis and Optimization, vol.38, no.7, pp.819-830, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 7
  • Publication Date: 2017
  • Doi Number: 10.1080/01630563.2016.1254654
  • Journal Name: Numerical Functional Analysis and Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.819-830
  • Keywords: Activation function, Borel measure, density, lightning bolt, neural network, orbit, orthogonal measure, weak convergence
  • Uşak University Affiliated: No

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.