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The Ethereal
Limitations on approximation by deep and shallow neural networks
November 30, 2022 ยท Declared Dead ยท ๐ Journal of machine learning research
"No code URL or promise found in abstract"
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Authors
Guergana Petrova, Przemysลaw Wojtaszczyk
arXiv ID
2212.02223
Category
stat.ML: Machine Learning (Stat)
Cross-listed
cs.LG,
math.FA
Citations
9
Venue
Journal of machine learning research
Last Checked
4 months ago
Abstract
We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approximate the functions in K when requiring the approximants to come from outputs of such networks. Our results are obtained as a byproduct of the study of the recently introduced Lipschitz widths.
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