Legendre Equivalences of Spherical Boltzmann Machines
Disordered Systems and Neural Networks
2020-02-19 v3 Mathematical Physics
math.MP
Abstract
We study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove the free energies of the spherical and Gaussian models are related by a Legendre transformation. Incidentally our analysis brings also a new purely variational derivation of the free energy of the spherical models.
Keywords
Cite
@article{arxiv.1910.14559,
title = {Legendre Equivalences of Spherical Boltzmann Machines},
author = {Giuseppe Genovese and Daniele Tantari},
journal= {arXiv preprint arXiv:1910.14559},
year = {2020}
}
Comments
typos corrected