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We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
Andrew R Barron · 1993
Earlier work this paper cites.
Why deep neural networks for function approximation?
Shiyu Liang and R Srikant · 2016
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Benefits of depth in neural networks
Matus Telgarsky · 2016
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The expressive power of neural networks: A view from the width
Zhou Lu, Hongming Pu, Feicheng Wang, Zhiqiang Hu, and Liwei Wang · 2017
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Deep relu networks lessen the curse of dimensionality
Hadrien Montanelli and Qiang Du · 2017
Cited alongside, same era.
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, and Qianli Liao · 2017
Later among the works it cites.
Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
Later among the works it cites.
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