Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines. (arXiv:2005.09424v2 [cond-mat.dis-nn] UPDATED)

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.

arxiv boltzmann energy free machines minimax