  In this article we identify a general class of high-dimensional continuous
functions that can be approximated by deep neural networks (DNNs) with the
rectified linear unit (ReLU) activation without the curse of dimensionality. In
other words, the number of DNN parameters grows at most polynomially in the
input dimension and the approximation error. The functions in our class can be
expressed as a potentially unbounded number of compositions of special
functions which include products, maxima, and certain parallelized Lipschitz
continuous functions.
