Journal:Informatica
Volume 21, Issue 3 (2010), pp. 339–348
Abstract
In the presented paper, some issues of the fundamental classical mechanics theory in the sense of Ising physics are introduced into the applied neural network area. The expansion of the neural networks theory is based primarily on introducing Hebb postulate into the mean field theory as an instrument of analysis of complex systems. Appropriate propositions and a theorem with proofs were proposed. In addition, some computational background is presented and discussed.
Journal:Informatica
Volume 20, Issue 4 (2009), pp. 477–486
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.