Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio