"Zakopane" . . . . "42241" . "10"^^ . . . "1"^^ . . . "RIV/67985807:_____/14:00427584" . "Representations of Highly-Varying Functions by One-Hidden-Layer Networks" . "Springer-Verlag" . . "[C976AF874B74]" . . . "Artificial Intelligence and Soft Computing Part I" . "Representations of Highly-Varying Functions by One-Hidden-Layer Networks"@en . "Limitations of capabilities of one-hidden-layer networks are investigated. It is shown that for networks with Heaviside perceptrons as well as for networks with kernel units used in SVM, there exist large sets of d-variable functions which cannot be tractably represented by these networks, i.e., their representations require numbers of units or sizes of weighs depending on d exponentially. Our results are derived using the concept of variational norm from nonlinear approximation theory and the concentration of measure property of high dimensional Euclidean spaces."@en . "0302-9743" . "Representations of Highly-Varying Functions by One-Hidden-Layer Networks"@en . "10.1007/978-3-319-07173-2_7" . . . "2014-06-01+02:00"^^ . . "I, P(LD13002)" . "RIV/67985807:_____/14:00427584!RIV15-AV0-67985807" . "Cham" . . . "K\u016Frkov\u00E1, V\u011Bra" . "model complexity of neural networks; one-hidden-layer networks; highly-varying functions; tractability of representations of multivariable functions by neural networks"@en . "000341246000007" . . . "978-3-319-07172-5" . . "Representations of Highly-Varying Functions by One-Hidden-Layer Networks" . "Limitations of capabilities of one-hidden-layer networks are investigated. It is shown that for networks with Heaviside perceptrons as well as for networks with kernel units used in SVM, there exist large sets of d-variable functions which cannot be tractably represented by these networks, i.e., their representations require numbers of units or sizes of weighs depending on d exponentially. Our results are derived using the concept of variational norm from nonlinear approximation theory and the concentration of measure property of high dimensional Euclidean spaces." . "1"^^ .