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

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• Sampling using $SU(N)$ gauge equivariant flows
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