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Author Barra, Adriano ♦ Guerra, Francesco
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2009-11-18
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics
Subject Keyword Condensed Matter - Disordered Systems and Neural Networks ♦ Condensed Matter - Statistical Mechanics ♦ physics:cond-mat
Abstract 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.
Description Reference: JOURNAL OF MATHEMATICAL PHYSICS 49, 125217 (2008)
Educational Use Research
Learning Resource Type Article
Page Count 15


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