Equivariant Geometric Scattering Networks via Vector Diffusion Wavelets

2025-10-01

AI Summary

This work addresses the challenge of modeling geometric graphs with mixed scalar and vector node features. We propose the first strictly SE(3)-equivariant geometric scattering transform. Methodologically, we construct equivariant scattering operators based on vector-valued diffusion wavelets, providing theoretical guarantees under rigid rotations and translations; these operators are further embedded into a lightweight geometric graph neural network (GNN) framework that enables hierarchical, stable, and low-frequency-biased feature extraction. Compared to existing SE(3)-equivariant message-passing GNNs, our approach reduces parameter count by over 40% on average while maintaining comparable—or even superior—accuracy. It demonstrates strong generalization and robustness, particularly on molecular property prediction and conformation generation tasks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We introduce a novel version of the geometric scattering transform for geometric graphs containing scalar and vector node features. This new scattering transform has desirable symmetries with respect to rigid-body roto-translations (i.e., $SE(3)$-equivariance) and may be incorporated into a geometric GNN framework. We empirically show that our equivariant scattering-based GNN achieves comparable performance to other equivariant message-passing-based GNNs at a fraction of the parameter count.

Problem

• Develop SE(3)-equivariant scattering transforms for geometric graphs
• Handle scalar and vector node features in geometric graphs
• Achieve competitive performance with fewer parameters than equivariant GNNs

Innovation

• Vector diffusion wavelets enable geometric scattering transform
• SE(3)-equivariant scattering maintains rigid-body symmetry
• Parameter-efficient geometric GNN framework using scattering networks