# On Universal Approximation by Neural Networks with Uniform Guarantees on Approximation of Infinite Dimensional Maps

3 Oct 2019William H. GussRuslan Salakhutdinov

The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors have shown various forms of the universality of both fixed depth and fixed width neural networks... (read more)

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