Nonclosedness of sets of neural networks in Sobolev spaces

DOI10.1016/j.neunet.2021.01.007arXiv2007.11730MaRDI QIDQ6078695

Emily J. King, Alex Cloninger, Scott Mahan

Publication date: 28 September 2023

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.11730

zbMATH Keywords

Sobolev spaceclosednessfixed-architecture neural networksneural network expressivity

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Cites Work

• Networks and the best approximation property
• Approximative compactness of linear combinations of characteristic functions
• Multilayer feedforward networks are universal approximators
• The higher derivatives of the inverse tangent function and rapidly convergent BBP-type formulas
• Approximation by superpositions of a sigmoidal function
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