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arXiv · 2106.08978

Pattern recognition in Deep Boltzmann machines

Elena Agliari·Linda Albanese·Francesco Alemanno·Alberto Fachechi
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Abstract

We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking. This result is accomplished rigorously exploiting interpolating techniques and recovering the expression already known for the replica-symmetry case. Further, we drop the restriction constraint by introducing intra-layer connections among spins and we show that the resulting system can be mapped into a modular Hopfield network, which is also addressed rigorously via interpolating techniques up to the first step of replica symmetry breaking.

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Elena Agliari, Linda Albanese, Francesco Alemanno, Alberto Fachechi. 2021-06-16. Pattern recognition in Deep Boltzmann machines. https://arxiv.org/abs/2106.08978

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