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Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

  • Published:2023-08 Issue: Volume:77 Page:101746
  • ISSN:0885-064X
  • Container-title:Journal of Complexity
  • language:en
  • Short-container-title:Journal of Complexity

Author:

Grohs Philipp,Ibragimov Shokhrukh,Jentzen Arnulf,Koppensteiner Sarah

Funder

Shenzhen Research Institute of Big Data

Deutsche Forschungsgemeinschaft

Austrian Science Fund

Publisher

Elsevier BV

Subject

Applied Mathematics,Control and Optimization,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,General Mathematics

Reference59 articles.

1. Special Functions;Andrews,1999

2. Neural net approximation;Barron,1992

3. Universal approximation bounds for superpositions of a sigmoidal function;Barron;IEEE Trans. Inf. Theory,1993

4. Approximation and estimation bounds for artificial neural networks;Barron;Mach. Learn.,1994

5. An overview on deep learning-based approximation methods for partial differential equations;Beck;Discrete Contin. Dyn. Syst., Ser. B,2023

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