Measure Theoretic Results for Approximation by Neural Networks with Limited Weights.

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. [ABSTRACT FROM PUBLISHER]