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  • 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.
  • 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)
Title
  • Representations of Highly-Varying Functions by One-Hidden-Layer Networks
  • Representations of Highly-Varying Functions by One-Hidden-Layer Networks (en)
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  • Representations of Highly-Varying Functions by One-Hidden-Layer Networks
  • Representations of Highly-Varying Functions by One-Hidden-Layer Networks (en)
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  • RIV/67985807:_____/14:00427584!RIV15-AV0-67985807
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  • 42241
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  • RIV/67985807:_____/14:00427584
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  • model complexity of neural networks; one-hidden-layer networks; highly-varying functions; tractability of representations of multivariable functions by neural networks (en)
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  • [C976AF874B74]
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  • Artificial Intelligence and Soft Computing Part I
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  • Kůrková, Věra
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  • 000341246000007
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  • 0302-9743
number of pages
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  • 10.1007/978-3-319-07173-2_7
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  • Springer-Verlag
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  • 978-3-319-07172-5
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