# Counting Phases and Faces Using Bayesian Thermodynamic Integration

arXiv: https://arxiv.org/abs/2206.07494 · HTML: https://mlsanity.com/paper/2206.07494/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 18 May 2022.

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

- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [U2-Net: Going Deeper with Nested U-Structure for Salient Object Detection](https://mlsanity.com/paper/2005.09007/) (2020)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [Dist-GAN: An Improved GAN using Distance Constraints](https://mlsanity.com/paper/1803.08887/) (2018)
- [Unveiling phase transitions with machine learning](https://mlsanity.com/paper/1904.01486/) (2019)

## Abstract (arXiv)

We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions over a space of external parameters and approximating the metric field by a Hessian of a convex function. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP without any a priori knowledge about microscopic rules of the models. We also demonstrate how our approach can be used to visualize the latent space of StyleGAN models and evaluate the variability of the generated images.