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

@article{Guss2019OnUA, title={On Universal Approximation by Neural Networks with Uniform Guarantees on Approximation of Infinite Dimensional Maps}, author={William H. Guss and R. Salakhutdinov}, journal={ArXiv}, year={2019}, volume={abs/1910.01545} }

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. However, in many cases, these classical results fail to extend to the recent use of approximations of neural networks with infinitely many units for functional… CONTINUE READING

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