# Expressive Power and Approximation Errors of Restricted Boltzmann Machines

arXiv: https://arxiv.org/abs/1406.3140 · HTML: https://mlsanity.com/paper/1406.3140/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2014.

## Built on by (most cited first, 4 of 4)

- [Expressive equivalence of classical and quantum restricted Boltzmann machines](https://mlsanity.com/paper/2502.17562/) (2025)
- [An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States](https://mlsanity.com/paper/2206.09241/) (2022)
- [Supermodular Rank: Set Function Decomposition and Optimization](https://mlsanity.com/paper/2305.14632/) (2023)
- [Distributional simplicity bias and effective convexity in Energy Based Models](https://mlsanity.com/paper/2605.07844/) (2026)

## Abstract (arXiv)

We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model with n visible and m hidden units is bounded from above by n - leftlfloor log(m+1) rightrfloor - fracm+12leftlfloorlog(m+1)rightrfloor ≈ (n -1) - log(m+1). In this way we can specify the number of hidden units that guarantees a sufficiently rich model containing different classes of distributions and respecting a given error tolerance.