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This article concerns the expressive power of depth in deep feed-forward neural nets with ReLU activations. Specifically, we answer the following question: for a fixed d_in≥ 1, what is the minimal width w so that neural nets with ReLU activations, input dimension d_in, hidden layer widths at most w, and arbitrary depth can approximate any continuous, real-valued function of d_in variables arbitrarily well? It turns out that this minimal width is exactly equal to d_in+1. That is, if all thearXiv:1710.11278v2 fatcat:aoluxiwi5jgzzc7w5fv42jpqj4