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

arXiv: https://arxiv.org/abs/1702.03260 · HTML: https://mlsanity.com/paper/1702.03260/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2017.

## Built on by (most cited first, 6 of 6)

- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [Inferring effective couplings with Restricted Boltzmann Machines](https://mlsanity.com/paper/2309.02292/) (2023)
- [Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physics](https://mlsanity.com/paper/2307.06797/) (2023)
- [Unsupervised hierarchical clustering using the learning dynamics of RBMs](https://mlsanity.com/paper/2302.01851/) (2023)
- [Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensions](https://mlsanity.com/paper/2505.18046/) (2025)
- [JSRNN: Joint Sampling and Reconstruction Neural Networks for High Quality Image Compressed Sensing](https://mlsanity.com/paper/2211.05963/) (2022)

## Abstract (arXiv)

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.