Measure Theoretic Results for Approximation by Neural Networks with Limited Weights

Ismailov V. E., Savas E.

Numerical Functional Analysis and Optimization, cilt.38, sa.7, ss.819-830, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 7
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/01630563.2016.1254654
  • Dergi Adı: Numerical Functional Analysis and Optimization
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.819-830
  • Anahtar Kelimeler: Activation function, Borel measure, density, lightning bolt, neural network, orbit, orthogonal measure, weak convergence
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.