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 problem of min–max type. In the absence of magnetic fields the order parameter is shown to exhibit a phase transition whose dependence on the geometry of the system is investigated.
The Solution of the Deep Boltzmann Machine on the Nishimori Line
Alberici D.;
2021
Abstract
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 problem of min–max type. In the absence of magnetic fields the order parameter is shown to exhibit a phase transition whose dependence on the geometry of the system is investigated.File in questo prodotto:
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15 Alberici, Camilli, Contucci, Mingione - CMP21 - The solution of the Deep Boltzmann Machine on the Nishimori line.pdf
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