Interpreting machine learning of topological quantum phase transitions

TL;DR

This paper demonstrates that shallow neural networks, guided by domain knowledge, can interpret topological quantum phase transitions by learning meaningful physical features, advancing the understanding of complex quantum systems.

Contribution

It shows that interpretable machine learning with shallow ANNs and domain knowledge can identify topological phases and features in quantum many-body problems.

Findings

ANN learns topological invariants

ANN identifies deconfinement of loops

Faithful phase diagrams constructed

Abstract

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. ``Interpretability'' remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? ``Interpretable'' machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $\mathbb{Z}_2$ topological insulator, and $\mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a ``domain knowledge''-guided approach to feature selection, facilitates the construction of faithful phase diagrams and semi-quantitative interpretation of the criteria in certain cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.