Alberici, DiegoCamilli, FrancescoContucci, PierluigiMingione, Emanuele2021-08-142021-08-142021-08-142021-07-2710.1007/s00220-021-04165-0https://infoscience.epfl.ch/handle/20.500.14299/180577WOS:000677940000002The 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.Physics, MathematicalPhysicsgriffiths inequalitiesfree-energyspinThe Solution of the Deep Boltzmann Machine on the Nishimori Linetext::journal::journal article::research article