Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov-Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks. (C) 2019 Published by Elsevier Ltd.