Lattice gauge equivariant convolutional neural networks

Abstract

We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.

letter: 6 pages, 5 figures; supplementary material: 14 pages, 4 figures; replaced some figures, added supplementary material

References in corpus (22)

• Properties and uses of the Wilson flow in lattice QCD
• QCD forces and heavy quark bound states
• Equivariant flow-based sampling for lattice gauge theory
• Neural Network Renormalization Group
• Sampling using $SU(N)$ gauge equivariant flows
• Highly-improved lattice field-strength tensor
• Regressive and generative neural networks for scalar field theory
• Improved staggered quark actions with reduced flavour symmetry violations for lattice QCD
• Spectral Reconstruction with Deep Neural Networks
• Machine learning action parameters in lattice quantum chromodynamics
• Improved Hamiltonian for Minkowski Yang-Mills Theory
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• Broken boost invariance in the Glasma via finite nuclei thickness
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Interpreting machine learning of topological quantum phase transitions
• Mapping distinct phase transitions to a neural network
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Gauge equivariant neural networks for quantum lattice gauge theories
• Improved lattice actions
• Progress on 3+1D Glasma simulations
• Implicit schemes for real-time lattice gauge theory

Cited by in corpus (18)

• Machine Learning in Nuclear Physics
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing
• Stochastic normalizing flows as non-equilibrium transformations
• Quantum field-theoretic machine learning
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• A method to challenge symmetries in data with self-supervised learning
• Fourier-Flow model generating Feynman paths
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Introduction to Normalizing Flows for Lattice Field Theory
• Homogeneous vector bundles and $G$-equivariant convolutional neural networks
• Deep Learning Hamiltonian Monte Carlo
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Gauge invariant input to neural network for path optimization method
• Improving efficiency of the path optimization method for a gauge theory
• Applications of Lattice Gauge Equivariant Neural Networks
• Gauge covariant neural network for quarks and gluons
• Large Language Models -- the Future of Fundamental Physics?