AdS-GNN -- a Conformally Equivariant Graph Neural Network
Maksim Zhdanov, Nabil Iqbal, Erik Bekkers, Patrick Forré·May 19, 2025
Summary
AdS-GNN, a neural network leveraging Anti de Sitter space, excels in computer vision and statistical physics, focusing on conformal equivariance. It addresses limitations by integrating all conformal transformations, emphasizing efficient architectures, geometric deep learning, and long-range graph benchmarking. Key aspects include decoupled weight decay, fast geometric deep learning, and conformal linear transformations. AdSd+1, a hyperboloid, supports a group action maintaining vector containment, crucial for conformal symmetry in machine learning. AdS-GNN outperforms EGNN in pixel segmentation, with similar PascalVOC-SP results. The text explores transformations in geometric algebra, focusing on ΓcΛ linking O0(p, q) to O0(p + 1, q + 1), with key equations detailing its role in mapping elements from Mp,q to themselves.
Introduction
Background
Overview of Anti de Sitter space and its relevance in theoretical physics
Brief history and current applications of neural networks in computer vision and statistical physics
Objective
Highlighting the unique capabilities of AdS-GNN in addressing limitations of existing models
Emphasizing the focus on conformal equivariance and its significance in machine learning
Method
Data Collection
Techniques for collecting data relevant to computer vision tasks
Methods for preparing data for AdS-GNN, considering its geometric nature
Data Preprocessing
Preprocessing steps to ensure data compatibility with AdS-GNN's architecture
Techniques for handling long-range dependencies in graph data
Efficient Architectures
Design considerations for AdS-GNN's architecture to support conformal equivariance
Implementation of decoupled weight decay for improved model performance
Fast Geometric Deep Learning
Overview of geometric deep learning principles
AdS-GNN's approach to fast geometric deep learning, focusing on its unique integration of Anti de Sitter space
Conformal Linear Transformations
Explanation of conformal linear transformations and their role in AdS-GNN
Discussion on how these transformations enhance the model's ability to handle geometric data
AdSd+1: A Hyperboloid Supporting Conformal Symmetry
Group Action and Vector Containment
Detailed explanation of the group action on AdSd+1
Importance of maintaining vector containment for preserving conformal symmetry
Implementation in AdS-GNN
How AdSd+1 is integrated into AdS-GNN to support efficient conformal transformations
Performance Evaluation
Comparison with EGNN
Detailed comparison of AdS-GNN with EGNN in pixel segmentation tasks
Analysis of similar PascalVOC-SP results to highlight AdS-GNN's performance
Benchmarking
Long-range graph benchmarking to assess AdS-GNN's effectiveness in handling complex graph structures
Transformations in Geometric Algebra
ΓcΛ and O0(p, q) to O0(p + 1, q + 1)
Detailed exploration of transformations in geometric algebra
Role of ΓcΛ in mapping elements from Mp,q to themselves, emphasizing its significance in AdS-GNN's operations
Conclusion
Summary of AdS-GNN's contributions
Future directions and potential applications
Implications for computer vision and statistical physics
Basic info
papers
high energy physics - theory
machine learning
artificial intelligence
Advanced features