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The solution of the deep Boltzmann machine on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational…
Stationarization and Multithermalization in spin glasses
Pierluigi Contucci, Federico Corberi, Jorge Kurchan +1
We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize…
The multi-species mean-field spin-glass on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions…
Annealing and replica-symmetry in Deep Boltzmann Machines
Diego Alberici, Adriano Barra, Pierluigi Contucci +1
In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interac…