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.
Alberici D., Camilli F., Contucci P., Mingione E. (2021). The Solution of the Deep Boltzmann Machine on the Nishimori Line. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 387(2), 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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