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Restricted Boltzmann machines (RBMs) are energy-based neural-networks whichare commonly used as the building blocks for deep architectures neuralarchitectures. In this work, we derive a deterministic framework for thetraining, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer(TAP) mean-field approximation of widely-connected systems with weakinteractions coming from spin-glass theory. While the TAP approach has beenextensively studied for fully-visible binary spin systems, our construction isgeneralized to latent-variable models, as well as to arbitrarily distributedreal-valued spin systems with bounded support. In our numerical experiments, wedemonstrate the effective deterministic training of our proposed models and areable to show interesting features of unsupervised learning which could not bedirectly observed with sampling. Additionally, we demonstrate how to utilizeour TAP-based framework for leveraging trained RBMs as joint priors indenoising problems.

A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines