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Representations of Highly-Varying Functions by One-Hidden-Layer Networks

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00427584" target="_blank" >RIV/67985807:_____/14:00427584 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1007/978-3-319-07173-2_7" target="_blank" >http://dx.doi.org/10.1007/978-3-319-07173-2_7</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-319-07173-2_7" target="_blank" >10.1007/978-3-319-07173-2_7</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Representations of Highly-Varying Functions by One-Hidden-Layer Networks

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    IN - Informatics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/LD13002" target="_blank" >LD13002: Modeling of complex systems for softcomputing methods</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2014

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Artificial Intelligence and Soft Computing Part I

  • ISBN

    978-3-319-07172-5

  • ISSN

    0302-9743

  • e-ISSN

  • Number of pages

    10

  • Pages from-to

    67-76

  • Publisher name

    Springer

  • Place of publication

    Cham

  • Event location

    Zakopane

  • Event date

    Jun 1, 2014

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000341246000007