Adriano Barra, Giuseppe Genovese, Francesco Guerra, Daniele Tantari
In this paper we continue our investigation on the high storage regime of the neural network with Gaussian patterns. Trough an exact mapping among its partition function and one of a bipartite spin glass (whose parties are made of by Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observable and their fluctuations as well as overlap fluctuations are achieved and discussed. Then, we move further, protracting such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two spin glass quenched free energies even in the replica symmetric framework.
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http://arxiv.org/abs/1205.3900
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