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

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.
Alberici D.; Camilli F.; Contucci P.; Mingione E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/862321
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