Global convergence and suppression of spurious states of the Hopfield neural networks

Author

Abe, Shigeo

Author_Institution

Hitachi, Ltd., Omika, Japan

Volume

40

Issue

4

fYear

1993

fDate

4/1/1993 12:00:00 AM

Firstpage

246

Lastpage

257

Abstract

Assuming that the output function of neurons is monotonic and differentiable at any interior point in the output range, the condition necessary for a vertex of a hypercube to become a local minimum of the Hopfield neural networks and the form of the convergence region to that minimum are clarified. Based on this, a method for analyzing and suppressing spurious states in the networks is derived. It is shown that all the spurious states of the traveling salesman problem (TSP) for the Hopfield original energy function can be suppressed by the method, and the validity of the method is demonstrated by computer simulations

Keywords

Hopfield neural nets; hypercube networks; operations research; optimisation; Hopfield neural networks; Hopfield original energy function; convergence region; hypercube; local minimum; neurons; output function; spurious states; traveling salesman problem; Circuits; Computer simulation; Constraint optimization; Convergence; Eigenvalues and eigenfunctions; Hopfield neural networks; Hypercubes; Neural networks; Neurons; Traveling salesman problems;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.224297

Filename

224297