# Boltzmann machines and energy-based models

arXiv: https://arxiv.org/abs/1708.06008 · HTML: https://mlsanity.com/paper/1708.06008/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2017.

## Built on by (most cited first, 5 of 5)

- [Bounds all around: training energy-based models with bidirectional bounds](https://mlsanity.com/paper/2111.00929/) (2021)
- [Coin Flipping Neural Networks](https://mlsanity.com/paper/2206.09182/) (2022)
- [Multi-view Kernel PCA for Time series Forecasting](https://mlsanity.com/paper/2301.09811/) (2023)
- [Topology-Aware Exploration of Energy-Based Models Equilibrium: Toric QC-LDPC Codes and Hyperbolic MET QC-LDPC Codes](https://mlsanity.com/paper/2401.14749/) (2024)
- [Exploring bidirectional bounds for minimax-training of Energy-based models](https://mlsanity.com/paper/2506.04609/) (2025)

## Abstract (arXiv)

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Hessian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in general intractable. This intractability motivates approximate methods, including Gibbs sampler and contrastive divergence, and tractable alternatives, namely energy-based models.