# Pattern reconstruction with restricted Boltzmann machines

arXiv: https://arxiv.org/abs/2205.07087 · HTML: https://mlsanity.com/paper/2205.07087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 14 May 2022.

## Builds on (most cited first, 9 of 9)

- [Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priors](https://mlsanity.com/paper/1702.05882/) (2017)
- [Emergence of Compositional Representations in Restricted Boltzmann Machines](https://mlsanity.com/paper/1611.06759/) (2016)
- [Learning Restricted Boltzmann Machines via Influence Maximization](https://mlsanity.com/paper/1805.10262/) (2018)
- [Restricted Boltzmann Machines as Models of Interacting Variables](https://mlsanity.com/paper/2103.15917/) (2021)
- [Efficiency of local learning rules in threshold-linear associative networks](https://mlsanity.com/paper/2007.12584/) (2020)
- [Learning Compositional Representations of Interacting Systems with Restricted Boltzmann Machines: Comparative Study of Lattice Proteins](https://mlsanity.com/paper/1902.06495/) (2019)
- [From Boltzmann Machines to Neural Networks and Back Again](https://mlsanity.com/paper/2007.12815/) (2020)
- [Local max-cut in smoothed polynomial time](https://mlsanity.com/paper/1610.04807/) (2016)
- [Recognition Capabilities of a Hopfield Model with Auxiliary Hidden Neurons](https://mlsanity.com/paper/2101.05247/) (2021)

## Abstract (arXiv)

Restricted Boltzmann machines are energy models made of a visible and a hidden layer. We identify an effective energy function describing the zero-temperature landscape on the visible units and depending only on the tail behaviour of the hidden layer prior distribution. Studying the location of the local minima of such an energy function, we show that the ability of a restricted Boltzmann machine to reconstruct a random pattern depends indeed only on the tail of the hidden prior distribution. We find that hidden priors with strictly super-Gaussian tails give only a logarithmic loss in pattern retrieval, while an efficient retrieval is much harder with hidden units with strictly sub-Gaussian tails; if the hidden prior has Gaussian tails, the retrieval capability is determined by the number of hidden units (as in the Hopfield model).