A universal training scheme and the resulting universality for machine learning phases

TL;DR

This paper demonstrates that simple, single-training neural networks like autoencoders and GANs can accurately identify critical points across various physical models, suggesting a universal approach to phase transition detection.

Contribution

It introduces a universal training scheme with minimal neural network architectures that effectively detect phase transitions in diverse models.

Findings

Neural networks trained on two configurations can determine critical points in multiple models.

Simple neural networks with minimal neurons can generalize across different phase transition systems.

The approach indicates most phase transitions may belong to the Ising universality class.

Abstract

An autoencoder (AE) and a generative adversarial networks (GANs) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons and both the generator and the discriminator of the GANs are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NN) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GANs have precisely determined the critical points of several models, including the three-dimensional (3D) classical $O(3)$ model, the two-dimensional (2D) generalized classical XY model, the 2D two-state Potts model, and the 1D Bose-Hubbard model. The results presented here as well as that shown in {\it Eur. Phys. J. Plus {\bf 136}, 1116 (2021)} suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since a NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.