Model Complexities of Shallow Networks Representing Highly Varying Functions

0446410 - ÚI 2016 RIV NL eng J - Článek v odborném periodiku
Kůrková, Věra - Sanguineti, M.
Model Complexities of Shallow Networks Representing Highly Varying Functions.
Neurocomputing. Roč. 171, 1 January (2016), s. 598-604. ISSN 0925-2312. E-ISSN 1872-8286
Grant CEP: GA MŠMT(CZ) LD13002
Grant ostatní: grant for Visiting Professors(IT) GNAMPA-INdAM
Institucionální podpora: RVO:67985807
Klíčová slova: shallow networks * model complexity * highly varying functions * Chernoff bound * perceptrons * Gaussian kernel units
Kód oboru RIV: IN - Informatika
Impakt faktor: 3.317, rok: 2016

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 these norms 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.
Trvalý link: http://hdl.handle.net/11104/0248405