Measure theoretic results for approximation by neural networks with limited weights

Vugar Ismailov, Ekrem Savas
4/4/2023
cs.LGmath.FA

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Abstract

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons.

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Cite this paper

@article{ismailov2023measure,
  title  = {Measure theoretic results for approximation by neural networks with limited weights},
  author = {Vugar Ismailov and Ekrem Savas},
  year   = {2023},
  eprint = {2304.01880},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.01880v1}
}

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