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.

翻译：格点规范等变卷积网络（L-CNNs）是一种能够应用于非阿贝尔格点规范理论且不破坏规范对称性的卷积神经网络框架。我们展示了如何为L-CNNs赋予全局群等变性，从而将其表述从仅对平移等变扩展为对全局格点对称性（如旋转和反射）也具有等变性。此外，我们提供了L-CNNs的几何表述，并揭示了L-CNNs中的卷积如何作为SU($N$)主丛上规范等变神经网络的特例而出现。