Lattice Gauge Equivariant Convolutional Neural Networks

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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.
Funding Information
  • Austrian Science Fund (P32446-N27, P28352, W1252-N27)
  • Nvidia

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