Geometrical aspects of lattice gauge equivariant convolutional neural networks
Journal article, 2024

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.

Author

David I. Müller

Vienna University of Technology

Jimmy Aronsson

Chalmers, Mathematical Sciences, Algebra and geometry

Daniel Schuh

Vienna University of Technology

Transactions on Machine Learning Research

28358856 (eISSN)

Vol. 2024

Subject Categories (SSIF 2025)

Geometry

Subatomic Physics

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Latest update

3/17/2025