Optimal Approximation Complexity of High-Dimensional Functions with Neural Networks

no code implementations • 30 Jan 2023 • Vincent P. H. Goverse, Jad Hamdan, Jared Tanner

We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of constant depth to arbitrary accuracy, demonstrating optimal order approximation rates across all nonlinear approximators, including standard ReLU networks.

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