A General Constructive Upper Bound on Shallow Neural Nets Complexity

Frantisek Hakl, Vit Fojtik
10/7/2025
stat.MLcs.LG

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Abstract

We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem, is constructive and more general than previous bounds of this character, as it applies to any continuous function on any compact set.

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Cite this paper

@article{hakl2025general,
  title  = {A General Constructive Upper Bound on Shallow Neural Nets Complexity},
  author = {Frantisek Hakl and Vit Fojtik},
  year   = {2025},
  eprint = {2510.06372},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2510.06372v1}
}

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