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.; Camilli F.; Contucci P.; Mingione E.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - ELETTRONICO. - 387:2(2021), pp. 1191-1214. [10.1007/s00220-021-04165-0]
The Solution of the Deep Boltzmann Machine on the Nishimori Line
Camilli F.
;Contucci P.;Mingione E.
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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