# Riemann-Theta Boltzmann Machine

arXiv: https://arxiv.org/abs/1712.07581 · HTML: https://mlsanity.com/paper/1712.07581/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2017.

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

- [Product Jacobi-Theta Boltzmann machines with score matching](https://mlsanity.com/paper/2303.05910/) (2023)
- [A Unified Theory of Exact Inference and Learning in Exponential Family Latent Variable Models](https://mlsanity.com/paper/2404.19501/) (2024)

## Abstract (arXiv)

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.