Can Two Hidden Layers Make a Difference?

Autoři: RNDr. Věra Kůrková, DSc.
Rok vydání: 2013
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Adaptive and Natural Computing Algorithms
Projekty: Učení funkcionálních vztahů z vysoce dimenzionálních dat
Bibliografická citace: KŮRKOVÁ, Věra, SANGUINETI, M. Can Two Hidden Layers Make a Difference? In: TOMASSINI, M., ANTONIONI, A., DAOLIO, F., BUESSER, P., eds. Adaptive and Natural Computing Algorithms. Berlin: Springer, 2013, S. 30-39. Lecture Notes in Computer Science, 7824. ISBN 978-3-642-37212-4. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-642-37213-1_4
DOI: 10.1007/978-3-642-37213-1_4
ID: 391257

Abstrakt

Representations of multivariable Boolean functions by one and two-hidden-layer Heaviside perceptron networks are investigated. Sufficient conditions are given for representations with the numbers of network units depending on the input dimension d linearly and polynomially. Functions with such numbers depending on d exponentially or having some weights exponentially large are described in terms of properties of their communication matrices. A mathematical formalization of the concept of “highly-varying functions” is proposed. There is given an example of such function which can be represented by a network with two hidden layers with merely d units.