AdS-GNN -- a Conformally Equivariant Graph Neural Network

• URL: http://arxiv.org/abs/2505.12880v1
• Date: Mon, 19 May 2025 09:08:52 GMT
• Title: AdS-GNN -- a Conformally Equivariant Graph Neural Network
• Authors: Maksim Zhdanov, Nabil Iqbal, Erik Bekkers, Patrick Forré,
• Abstract summary: We build a neural network that is equivariant under general conformal transformations.<n>We validate our model on tasks from computer vision and statistical physics.
• Score: 9.96018310438305
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

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