On the universal approximation property of radial basis function neural networks

Aysu Ismayilova, Muhammad Ismayilov
4/5/2023
cs.LGstat.ML

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Abstract

In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the $d$-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.

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Cite this paper

@article{ismayilova2023universal,
  title  = {On the universal approximation property of radial basis function neural networks},
  author = {Aysu Ismayilova and Muhammad Ismayilov},
  year   = {2023},
  eprint = {2304.02220},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.02220v2}
}

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