Incorporating gauge-invariance in equivariant networks
Keywords: gauge-invariance, gauge theories, equivariance
Abstract: Gauge theories, which describe fundamental forces in nature, arise from the principle of locality in physical interactions. These theories are characterized by their invariance under local symmetry transformations and the presence of a gauge field that mediates interactions. While recent works have introduced gauge equivariant neural networks, these models often focus on specific cases like tangent bundles or quotient spaces, limiting their applicability to the diverse gauge theories in physics. We propose a novel architecture for learning general gauge invariant quantities by explicitly modeling the gauge field in the context of graph neural networks. Our framework fills a critical gap in the existing literature by providing a general recipe for gauge invariance without restrictions on the fiber spaces. This approach allows for the modeling of more complex gauge theories, such as those with $SU(N)$ gauge groups, which are prevalent in particle physics. We evaluate our method on classical physical systems, including the XY model on various curved geometries, demonstrating its ability to capture gauge invariant properties in settings where existing equivariant architectures fall short. Our work takes a significant step towards bridging the gap between gauge theories in physics and equivariant neural network architectures, opening new avenues for applying machine learning to fundamental physical problems.
Primary Area: learning on graphs and other geometries & topologies
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 13044
Loading