# Discrete Restricted Boltzmann Machines

arXiv: https://arxiv.org/abs/1301.3529 · HTML: https://mlsanity.com/paper/1301.3529/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [Identifiability of Product of Experts Models](https://mlsanity.com/paper/2310.09397/) (2023)
- [Quantitative Universal Approximation Bounds for Deep Belief Networks](https://mlsanity.com/paper/2208.09033/) (2022)

## Abstract (arXiv)

We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in these models in terms of configurations of projected products of simplices and normal fans of products of simplices. We bound the number of hidden variables, depending on the cardinalities of their state spaces, for which these models can approximate any probability distribution on their visible states to any given accuracy. In addition, we use algebraic methods and coding theory to compute their dimension.