Measure Theoretic Results for Approximation by Neural Networks with Limited Weights. (3rd July 2017) - Ismailov, Vugar E.; Savas, Ekrem
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.