Model Complexities of Shallow Networks Representing Highly Varying Functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00446410" target="_blank" >RIV/67985807:_____/16:00446410 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.neucom.2015.07.014" target="_blank" >http://dx.doi.org/10.1016/j.neucom.2015.07.014</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.neucom.2015.07.014" target="_blank" >10.1016/j.neucom.2015.07.014</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Model Complexities of Shallow Networks Representing Highly Varying Functions

Popis výsledku v původním jazyce

Model complexities of shallow (i.e., one-hidden-layer) networks representing highly varying multivariable {-1,1}{-1,1}-valued functions are studied in terms of variational norms tailored to dictionaries of network units. It is shown that bounds on thesenorms define classes of functions computable by networks with constrained numbers of hidden units and sizes of output weights. Estimates of probabilistic distributions of values of variational norms with respect to typical computational units, such as perceptrons and Gaussian kernel units, are derived via geometric characterization of variational norms combined with the probabilistic Chernoff Bound. It is shown that almost any randomly chosen {-1,1}{-1,1}-valued function on a sufficiently large d-dimensional domain has variation with respect to perceptrons depending on d exponentially.

Název v anglickém jazyce

Model Complexities of Shallow Networks Representing Highly Varying Functions

Popis výsledku anglicky

Model complexities of shallow (i.e., one-hidden-layer) networks representing highly varying multivariable {-1,1}{-1,1}-valued functions are studied in terms of variational norms tailored to dictionaries of network units. It is shown that bounds on thesenorms define classes of functions computable by networks with constrained numbers of hidden units and sizes of output weights. Estimates of probabilistic distributions of values of variational norms with respect to typical computational units, such as perceptrons and Gaussian kernel units, are derived via geometric characterization of variational norms combined with the probabilistic Chernoff Bound. It is shown that almost any randomly chosen {-1,1}{-1,1}-valued function on a sufficiently large d-dimensional domain has variation with respect to perceptrons depending on d exponentially.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

<a href="/cs/project/LD13002" target="_blank" >LD13002: Modelování složitých systémů softcomputingovými metodami</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Neurocomputing

ISSN

0925-2312

e-ISSN

—

Svazek periodika

171

Číslo periodika v rámci svazku

1 January

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

598-604

Kód UT WoS článku

000364883900062

EID výsledku v databázi Scopus

2-s2.0-84947029082