Complexity of Shallow Networks Representing Functions with Large Variations

  • Věra Kůrková
  • Marcello Sanguineti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8681)


Model complexities of networks representing multivariable functions is studied in terms of variational norms tailored to types of network units. It is shown that the size of the variational norm reflects both the number of hidden units and sizes of output weights. Lower bounds on growth of variational norms with increasing input dimension d are derived for Gaussian units and perceptrons. It is proven that variation of the d-dimensional parity with respect to Gaussian Support Vector Machines grows exponentially with d and for large values of d, almost any randomly-chosen Boolean function has variation with respect to perceptrons depending on d exponentially.


One-hidden-layer networks model complexity representations of multivariable functions perceptrons Gaussian SVMs 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Věra Kůrková
    • 1
  • Marcello Sanguineti
    • 2
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPragueCzech Republic
  2. 2.DIBRISUniversity of GenoaGenovaItaly

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