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.
Legendre equivalences of spherical Boltzmann machines / Genovese G.; Tantari D.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - ELETTRONICO. - 53:9(2020), pp. 094001.1-094001.18. [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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