# Approximate sampling and estimation of partition functions using neural networks

arXiv: https://arxiv.org/abs/2209.10423 · HTML: https://mlsanity.com/paper/2209.10423/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 11 of 11)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Spectral redemption: clustering sparse networks](https://mlsanity.com/paper/1306.5550/) (2013)
- [The Computer Science and Physics of Community Detection: Landscapes, Phase Transitions, and Hardness](https://mlsanity.com/paper/1702.00467/) (2017)
- [Learning the Ising Model with Generative Neural Networks](https://mlsanity.com/paper/2001.05361/) (2020)
- [Variational Autoencoder Analysis of Ising Model Statistical Distributions and Phase Transitions](https://mlsanity.com/paper/2104.06368/) (2021)

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

- [Targeting the partition function of chemically disordered materials with a generative approach based on inverse variational autoencoders](https://mlsanity.com/paper/2408.14928/) (2024)
- [Thermodynamic properties of chemically disordered compounds via AI-driven estimation of partition function with the PULSE method](https://mlsanity.com/paper/2605.28594/) (2026)

## Abstract (arXiv)

We consider the closely related problems of sampling from a distribution known up to a normalizing constant, and estimating said normalizing constant. We show how variational autoencoders (VAEs) can be applied to this task. In their standard applications, VAEs are trained to fit data drawn from an intractable distribution. We invert the logic and train the VAE to fit a simple and tractable distribution, on the assumption of a complex and intractable latent distribution, specified up to normalization. This procedure constructs approximations without the use of training data or Markov chain Monte Carlo sampling. We illustrate our method on three examples: the Ising model, graph clustering, and ranking.