Lattice Gauge Equivariant Convolutional Neural Networks

Dec 23, 2020
6 pages
Published in:
  • Phys.Rev.Lett. 128 (2022) 3, 3
  • Published: Jan 20, 2022
e-Print:

Citations per year

2020202120222023202405101520
Abstract: (APS)
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.
Note:
  • letter: 6 pages, 5 figures; supplementary material: 14 pages, 4 figures; replaced some figures, added supplementary material
  • gauge: covariance
  • invariance: gauge
  • lattice
  • neural network
  • lattice field theory
  • gauge field theory
  • Polyakov loop
  • topological
  • Wilson loop
  • structure