On the capabilities of higher-order neurons: a radial basis function approach
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Higher-order neurons with $k$ monomials in $n$ variables are shown to have Vapnik-Chervonenkis (VC) dimension at least $nk+1$. This result supersedes the previously known lower bound obtained via $k$-term monotone disjunctive normal form (DNF) formulas. Moreover, it implies that the VC dimension of higher-order neurons with $k$ monomials is strictly larger than the VC dimension of $k$-term monotone DNF. The result is achieved by introducing an exponential approach that employs Gaussian radial basis function (RBF) neural networks for obtaining classifications of points in terms of higher-order neurons.
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