Sparsity and Complexity of Networks Computing Highly-Varying Functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00493825" target="_blank" >RIV/67985807:_____/18:00493825 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-030-01424-7_52" target="_blank" >http://dx.doi.org/10.1007/978-3-030-01424-7_52</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-01424-7_52" target="_blank" >10.1007/978-3-030-01424-7_52</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sparsity and Complexity of Networks Computing Highly-Varying Functions

Popis výsledku v původním jazyce

Approximative measures of network sparsity in terms of norms tailored to dictionaries of computational units are investigated. Lower bounds on these norms of real-valued functions on finite domains are derived. The bounds are proven by combining the concentration of measure property of high-dimensional spaces with characterization of dictionaries of computational units in terms of their capacities and coherence measured by their covering numbers. The results are applied to dictionaries used in neurocomputing which have power-type covering numbers. Probabilistic results are illustrated by a concrete construction of a class of functions, computation of which by perceptron networks requires large number of units or it is unstable due to large output weights.

Název v anglickém jazyce

Sparsity and Complexity of Networks Computing Highly-Varying Functions

Popis výsledku anglicky

Approximative measures of network sparsity in terms of norms tailored to dictionaries of computational units are investigated. Lower bounds on these norms of real-valued functions on finite domains are derived. The bounds are proven by combining the concentration of measure property of high-dimensional spaces with characterization of dictionaries of computational units in terms of their capacities and coherence measured by their covering numbers. The results are applied to dictionaries used in neurocomputing which have power-type covering numbers. Probabilistic results are illustrated by a concrete construction of a class of functions, computation of which by perceptron networks requires large number of units or it is unstable due to large output weights.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA18-23827S" target="_blank" >GA18-23827S: Schopnosti a omezení mělkých a hlubokých sítí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

Artificial Neural Networks and Machine Learning – ICANN 2018. Proceedings, Part III

ISBN

978-3-030-01423-0

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

10

Strana od-do

534-543

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Rhodes

Datum konání akce

4. 10. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—