Geometrical aspects of lattice gauge equivariant convolutional neural networks

Understand

Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry.

• We demonstrate how L-CNNs can be equipped with global group equivariance.
• This allows us to extend the formulation to be equivariant not just under translations but under global lattice symmetries such as rotations and reflections.
• Additionally, we provide a geometric formulation of L-CNNs and show how convolutions in L-CNNs arise as a special case of gauge equivariant neural networks on SU($N$) principal bundles.