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 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.

arXiv comment9 pages, 11 figures

References in corpus (34)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anyons in an exactly solved model and beyond
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Many-body quantum state tomography with neural networks
• Quantum Entanglement in Neural Network States
• On A Proper Definition of Spin Current
• Machine learning quantum phases of matter beyond the fermion sign problem
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Mapping topological order in coordinate space
• Identifying topological order through unsupervised machine learning
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning Phases of Strongly Correlated Fermions
• Symmetries and many-body excited states with neural-network quantum states
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Kernel methods for interpretable machine learning of order parameters
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Self-Learning Monte Carlo Method in Fermion Systems
• Deep Learning Topological Invariants of Band Insulators
• Probing hidden spin order with interpretable machine learning
• Unsupervised identification of topological order using predictive models
• Machine learning action parameters in lattice quantum chromodynamics
• Learning multiple order parameters with interpretable machines
• Interpretable Machine Learning Study of Many-Body Localization Transition in Disordered Quantum Ising Spin Chains
• Unsupervised learning using topological data augmentation
• Emergent Quantum Mechanics in an Introspective Machine Learning Architecture
• Visualizing Neural Network Developing Perturbation Theory

Cited by in corpus (29)

• Provably efficient machine learning for quantum many-body problems
• Machine Learning for Quantum Matter
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Unsupervised machine learning of topological phase transitions from experimental data
• Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
• Lattice gauge equivariant convolutional neural networks
• Machine learning topological phases in real space
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Machine learning topological invariants of non-Hermitian systems
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Conserved current of nonconserved quantities
• Phase Detection with Neural Networks: Interpreting the Black Box
• Interpretable and unsupervised phase classification
• Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials
• Machine learning non-Hermitian topological phases
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms
• Unsupervised Machine Learning of Quenched Gauge Symmetries: A Proof-of-Concept Demonstration
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
• Identifying topology of leaky photonic lattices with machine learning
• Efficient and quantum-adaptive machine learning with fermion neural networks
• Quaternion-based machine learning on topological quantum systems
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Fluctuation based interpretable analysis scheme for quantum many-body snapshots
• Learning phases with Quantum Monte Carlo simulation cell
• Learning quantum symmetries with interactive quantum-classical variational algorithms
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Attention to Quantum Complexity