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：晶格规范等变卷积神经网络的几何方面 翻译后摘要： 晶格规范等变卷积神经网络（L-CNN）是一种卷积神经网络的框架，可应用于非阿贝尔晶格规范理论，而不会违反规范对称性。我们展示了如何为L-CNN提供全局群等变性。这使我们能够将该公式扩展为不仅在平移下等变，而且在全局晶格对称性诸如旋转和反射下等变。此外，我们提供了L-CNN的几何公式，并展示了L-CNN中的卷积如何成为SU（$N$）主丛上规范等变神经网络的特殊情况。