Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax formula for the replica symmetric free energy of deep restricted
  Boltzmann machines   We study the free energy of a most used deep architecture for restricted
Boltzmann machines, where the layers are disposed in series. Assuming
independent Gaussian distributed random weights, we show that the error term in
the so-called replica symmetric sum rule can be optimised as a saddle point.
This leads us to conjecture that in the replica symmetric approximation the
free energy is given by a min max formula, which parallels the one achieved for
two-layer case.

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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph