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Title: Interpreting machine learning of topological quantum phase transitions

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 nonlinear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, Z2 topological insulator, and Z2 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 semiquantitative 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.

Authors:
ORCiD logo; ; ORCiD logo
Publication Date:
Research Org.:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
OSTI Identifier:
1632033
Alternate Identifier(s):
OSTI ID: 1733302
Grant/Contract Number:  
SC0018946
Resource Type:
Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 2; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Machine learning; Topological insulators; Topological phases of matter; Artificial neural networks

Citation Formats

Zhang, Yi, Ginsparg, Paul, and Kim, Eun-Ah. Interpreting machine learning of topological quantum phase transitions. United States: N. p., 2020. Web. doi:10.1103/PhysRevResearch.2.023283.
Zhang, Yi, Ginsparg, Paul, & Kim, Eun-Ah. Interpreting machine learning of topological quantum phase transitions. United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023283
Zhang, Yi, Ginsparg, Paul, and Kim, Eun-Ah. Thu . "Interpreting machine learning of topological quantum phase transitions". United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023283.
@article{osti_1632033,
title = {Interpreting machine learning of topological quantum phase transitions},
author = {Zhang, Yi and Ginsparg, Paul and Kim, Eun-Ah},
abstractNote = {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 nonlinear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, Z2 topological insulator, and Z2 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 semiquantitative 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.},
doi = {10.1103/PhysRevResearch.2.023283},
journal = {Physical Review Research},
number = 2,
volume = 2,
place = {United States},
year = {2020},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
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DOI: https://doi.org/10.1103/PhysRevResearch.2.023283

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