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Legendre Equivalences of Spherical Boltzmann Machines

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.

preprint2020arXivOpen access
Giuseppe GenoveseDaniele Tantari
math-phmath.MPcond-mat.dis-nn
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Giuseppe GenoveseDaniele Tantari

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