# Advanced Mean Field Theory of Restricted Boltzmann Machine

arXiv: https://arxiv.org/abs/1502.00186 · HTML: https://mlsanity.com/paper/1502.00186/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2015.

## Built on by (most cited first, 3 of 3)

- [Boltzmann machines as two-dimensional tensor networks](https://mlsanity.com/paper/2105.04130/) (2021)
- [Exploring Loss Landscapes through the Lens of Spin Glass Theory](https://mlsanity.com/paper/2407.20724/) (2024)
- [Fundamental operating regimes, hyper-parameter fine-tuning and glassiness: towards an interpretable replica-theory for trained restricted Boltzmann machines](https://mlsanity.com/paper/2406.09924/) (2024)

## Abstract (arXiv)

Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message passing based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling based method.