AdS-GNN -- a Conformally Equivariant Graph Neural Network

2025/05/19 by Maksim Zhdanov, Nabil Iqbal, Zhdanov, Maksim +5 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Graph Neural Networks #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2505.12880

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Probing Equivariance and Symmetry Breaking in Convolutional Networks
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• Large N Field Theories, String Theory and Gravity
• The Holographic Bound in Anti-de Sitter Space
• The Large N Limit of Superconformal Field Theories and Supergravity

Cited by

• Bridging Symmetry and Robustness: On the Role of Equivariance in Enhancing Adversarial Robustness

Related

• Symmetry-driven graph neural networks
• Geometrically Equivariant Graph Neural Networks: A Survey
• Neural Isometries: Taming Transformations for Equivariant ML
• Conformal Fields from Neural Networks
• Relaxed Equivariant Graph Neural Networks