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

## TL;DR

This paper introduces a deterministic, TAP-based framework for training and utilizing RBMs, extending their applicability to various data types and enabling new insights into unsupervised learning and denoising tasks.

## Contribution

It generalizes the TAP mean-field approach to latent-variable and real-valued RBMs, providing a deterministic alternative to sampling-based training methods.

## Key findings

- Effective deterministic training demonstrated on various RBMs.
- Revealed new features of unsupervised learning through TAP-based analysis.
- Applied RBMs as priors in denoising problems successfully.

## Abstract

Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field approximation of widely-connected systems with weak interactions coming from spin-glass theory. While the TAP approach has been extensively studied for fully-visible binary spin systems, our construction is generalized to latent-variable models, as well as to arbitrarily distributed real-valued spin systems with bounded support. In our numerical experiments, we demonstrate the effective deterministic training of our proposed models and are able to show interesting features of unsupervised learning which could not be directly observed with sampling. Additionally, we demonstrate how to utilize our TAP-based framework for leveraging trained RBMs as joint priors in denoising problems.