Random interactions in higher order neural networks

Author

Baldi, Pierre ; Venkatesh, Santosh S.

Author_Institution

Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA

Volume

39

Issue

1

fYear

1993

fDate

1/1/1993 12:00:00 AM

Firstpage

274

Lastpage

283

Abstract

Recurrent networks of polynomial threshold elements with random symmetric interactions are studied. Precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability. In particular, it is shown that there is a critical range of margins of stability (depending on the degree of polynomial interaction) such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network, while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network. The random energy model is also briefly examined, and links with higher-order neural networks and higher-order spin glass models are made explicit

Keywords

polynomials; random processes; recurrent neural nets; higher order neural networks; higher-order spin glass models; margin of stability; number of fixed points; polynomial threshold elements; random energy model; random symmetric interactions; recurrent networks; Asymptotic stability; Computer applications; Computer networks; Glass; Information processing; Intelligent networks; Mathematical model; Neural networks; Neurons; Polynomials;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.179374

Filename

179374