We study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove that 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.
Genovese G., Tantari D. (2020). Legendre equivalences of spherical Boltzmann machines. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 53(9), 1-18 [10.1088/1751-8121/ab6b92].
Legendre equivalences of spherical Boltzmann machines
Tantari D.
2020
Abstract
We study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove that 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.File in questo prodotto:
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