Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-11-18
JOURNAL OF MATHEMATICAL PHYSICS 49, 125217 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
15 pages
Scientific paper
In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage case, when the number of patterns is linearly diverging with the number of neurons. We study the infinite volume behavior of the normalized momenta of the partition function. We find a region in the parameter space where the free energy density in the infinite volume limit is self-averaging around its annealed approximation, as well as the entropy and the internal energy density. Moreover, we evaluate the corrections to their extensive counterparts with respect to their annealed expressions. The fluctuations of properly introduced overlaps, which act as order parameters, are also discussed.
Barra Adriano
Guerra Francesco
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