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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The authors would like to thank the anonymous reviewers for their insightful comments and suggestions, which helped to improve the quality of the paper.
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Aysu Ismayilova wrote Section 2. Muhammad Ismayilov wrote Section 3. Both authors wrote Section 1 and reviewed the manuscript.
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Ismayilova, A., Ismayilov, M. On the universal approximation property of radial basis function neural networks. Ann Math Artif Intell 92, 691–701 (2024). https://doi.org/10.1007/s10472-023-09901-x
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DOI: https://doi.org/10.1007/s10472-023-09901-x