The solution of the deep Boltzmann machine on the Nishimori line
Mathematical Physics
2021-08-18 v2 Disordered Systems and Neural Networks
math.MP
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.
Keywords
Cite
@article{arxiv.2012.13987,
title = {The solution of the deep Boltzmann machine on the Nishimori line},
author = {Diego Alberici and Francesco Camilli and Pierluigi Contucci and Emanuele Mingione},
journal= {arXiv preprint arXiv:2012.13987},
year = {2021}
}
Comments
30 pages, 1 figure. To appear in Communications in Mathematical Physics