# Restricted Boltzmann Machines: Introduction and Review

arXiv: https://arxiv.org/abs/1806.07066 · HTML: https://mlsanity.com/paper/1806.07066/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 14 of 14)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2105.13889/) (2021)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Most ReLU Networks Admit Identifiable Parameters](https://mlsanity.com/paper/2605.03601/) (2026)
- [Identifiability of Product of Experts Models](https://mlsanity.com/paper/2310.09397/) (2023)
- [Towards Transfer Learning for Large-Scale Image Classification Using Annealing-based Quantum Boltzmann Machines](https://mlsanity.com/paper/2311.15966/) (2023)
- [Constraining the outputs of ReLU neural networks](https://mlsanity.com/paper/2508.03867/) (2025)
- [Three Learning Stages and Accuracy-Efficiency Tradeoff of Restricted Boltzmann Machines](https://mlsanity.com/paper/2209.00873/) (2022)
- [On the Equality of the ELBO to a Sum of Entropies at Stationary Points of Learning](https://mlsanity.com/paper/2209.03077/) (2022)
- [Dynamic neuron approach to deep neural networks: Decoupling neurons for renormalization group analysis](https://mlsanity.com/paper/2410.00396/) (2024)
- [Quantitative Universal Approximation Bounds for Deep Belief Networks](https://mlsanity.com/paper/2208.09033/) (2022)
- [Structural Restricted Boltzmann Machine for image denoising and classification](https://mlsanity.com/paper/2306.09628/) (2023)
- [Absolute abstraction: a renormalisation group approach](https://mlsanity.com/paper/2407.01656/) (2024)
- [AI and Generative AI Transforming Disaster Management: A Survey of Damage Assessment and Response Techniques](https://mlsanity.com/paper/2505.08202/) (2025)

## Abstract (arXiv)

The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Boltzmann machines carry a rich structure, with connections to geometry, applied algebra, probability, statistics, machine learning, and other areas. The analysis of these models is attractive in its own right and also as a platform to combine and generalize mathematical tools for graphical models with hidden variables. This article gives an introduction to the mathematical analysis of restricted Boltzmann machines, reviews recent results on the geometry of the sets of probability distributions representable by these models, and suggests a few directions for further investigation.