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Nonlinear Approximation and (Deep) ReLU Networks · Around

2019

Nonlinear Approximation and (Deep) ReLU Networks

Daubechies, I., DeVore, R., Foucart, S. et al.

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This article is concerned with the approximation and expressive powers of deep neural networks.

This is an active research area currently producing many interesting papers.
The results most commonly found in the literature prove that neural networks approximate functions with classical smoothness to the same accuracy as classical linear methods of approximation, e.g.
approximation by polynomials or by piecewise polynomials on prescribed partitions.

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