Legendre Equivalences of Spherical Boltzmann Machines

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.

typos corrected

References in corpus (2)

• Free energy and complexity of spherical bipartite models
• Legendre Duality of Spherical and Gaussian Spin Glasses

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• A remark on the spherical bipartite spin glass