Embedded Patterns, Indirect Couplings with Randomness, and Memory Capacity in Neural Networks

Article type: Research Article

Authors: Garliauskas, Algis

Affiliations: Institute of Mathematics and Informatics, Akademijos 4, LT-06883, Vilnius, Lithuania, e-mail: galgis_1@ktl.mii.lt

Abstract: In the present paper, the neural networks theory based on presumptions of the Ising model is considered. Indirect couplings, the Dirac distributions and the corrected Hebb rule are introduced and analyzed. The embedded patterns memorized in a neural network and the indirect couplings are considered as random. Apart from the complex theory based on Dirac distributions the simplified stationary mean field equations and their solutions taking into account an ergodicity of the average overlap and the indirect order parameter are presented. The modeling results are demonstrated to corroborate theoretical statements and applied aspects.

Keywords: neural network, free energy density, Dirac distribution, memory capacity, ergodicity

Journal: Informatica, vol. 20, no. 4, pp. 477-486, 2009