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

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>

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
—

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

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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

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