The solution of the deep Boltzmann machine on the Nishimori line

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.

30 pages, 1 figure. To appear in Communications in Mathematical Physics