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

Deep neural network approximation of composite functions without the curse of dimensionality