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Updated: Aug 6, 2026

Basics of Multivariate Analysis in Neuroimaging Data
Published on: July 24, 2010
Descartes' rule of signs for radial basis function neural networks
1Lehrstuhl Mathematik und Informatik, Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany. mschmitt@lmi.ruhr-uni-bochum.de
Abstract:
We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the Vapnik-Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two or more input nodes have superlinear VC dimension. The rules also give rise to lower bounds for network sizes, thus demonstrating the relevance of network parameters for the complexity of computing with RBF neural networks.
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