Threestate neural network: from mutual information to the hamiltonian
Abstract
The mutual information, I, of the threestate neural network can be obtained exactly for the meanfield architecture, as a function of three macroscopic parameters: the overlap, the neural activity and the {\em activityoverlap}, i.e. the overlap restricted to the active neurons. We perform an expansion of I on the overlap and the activityoverlap, around their values for neurons almost independent on the patterns. From this expansion we obtain an expression for a Hamiltonian which optimizes the retrieval properties of this system. This Hamiltonian has the form of a disordered BlumeEmeryGriffiths model. The dynamics corresponding to this Hamiltonian is found. As a special characteristic of such network, we see that information can survive even if no overlap is present. Hence the basin of attraction of the patterns and the retrieval capacity is much larger than for the Hopfield network. The extreme diluted version is analized, the curves of information are plotted and the phase diagrams are built.
 Publication:

arXiv eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:condmat/9912328
 Bibcode:
 1999cond.mat.12328D
 Keywords:

 Statistical Mechanics;
 Disordered Systems and Neural Networks
 EPrint:
 10 pages (including 6 postscript figures)