ML Anthology

Limitations on Approximation by Deep and Shallow Neural Networks

Guergana Petrova, Przemyslaw Wojtaszczyk
JMLR 2023 pp. 1-38
/jmlr/2023/petrova2023jmlr-limitations/

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 estimates from below 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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Cite

Text

Petrova and Wojtaszczyk. "Limitations on Approximation by Deep and Shallow Neural Networks." Journal of Machine Learning Research, 2023.

Markdown

[Petrova and Wojtaszczyk. "Limitations on Approximation by Deep and Shallow Neural Networks." Journal of Machine Learning Research, 2023.](https://mlanthology.org/jmlr/2023/petrova2023jmlr-limitations/)

BibTeX

@article{petrova2023jmlr-limitations,
  title     = {{Limitations on Approximation by Deep and Shallow Neural Networks}},
  author    = {Petrova, Guergana and Wojtaszczyk, Przemyslaw},
  journal   = {Journal of Machine Learning Research},
  year      = {2023},
  pages     = {1-38},
  volume    = {24},
  url       = {https://mlanthology.org/jmlr/2023/petrova2023jmlr-limitations/}
}