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Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks

Authors:	Aleksandr Beknazaryan

Affiliation:	Institute of Environmental and Agricultural Biology (X-BIO), University of Tyumen, Volodarskogo 6, 625003 Tyumen, Russia;

Abstract:	We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on $1 / ε$ can $ε$ -approximate functions that are analytic on certain regions of $C^{d}$ .

Keywords:	deep neural networks analytic functions path norm regularization exponential convergence