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arXiv · 1910.14559

Legendre Equivalences of Spherical Boltzmann Machines

Giuseppe Genovese·Daniele Tantari
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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.

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Giuseppe Genovese, Daniele Tantari. 2019-10-31. Legendre Equivalences of Spherical Boltzmann Machines. https://doi.org/10.1088/1751-8121%2Fab6b92

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