Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines

Giuseppe Genovese

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arXiv · 2005.09424

Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines

Giuseppe Genovese

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Abstract

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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cond-mat.dis-nn cs.LG math.PR

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Giuseppe Genovese. 2020-05-15. Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines. https://arxiv.org/abs/2005.09424

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