Constructive Deep ReLU Neural Network Approximation

We propose an efficient, deterministic algorithm for constructing exponentially convergent deep neural network (DNN) approximations of multivariate, analytic maps f : [ - 1 , 1 ] K → R . We address in particular networks with the rectified linear unit (ReLU) activation function. Similar results and...

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Bibliographic Details
Published in:	Journal of scientific computing Vol. 90; no. 2; p. 75
Main Authors:	Herrmann, Lukas, Opschoor, Joost A. A., Schwab, Christoph
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.02.2022 Springer Nature B.V
Subjects:	Accuracy Algorithms Approximation Artificial neural networks Computational Mathematics and Numerical Analysis Convergence Fourier transforms Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Neural networks Optimization Partial differential equations Polynomials Theoretical Exponential convergence Deep ReLU neural networks 41A10 65D05 Neural network construction Generalization error 41A50 65D15
ISSN:	0885-7474, 1573-7691
Online Access:	Get full text
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