Advances in Graph Neural Networks and Geometric Deep Learning

The field of graph neural networks and geometric deep learning is rapidly evolving, with a focus on developing innovative methods for graph representation learning, subgraph matching, and graph similarity computation. Recent research has explored the use of geometric and topological techniques, such as discrete Ricci flow and Euler Characteristic Transform, to improve the performance and interpretability of graph neural networks. Additionally, there is a growing interest in developing equivariant models that can handle rigid-body transformations and preserve geometric structures. Noteworthy papers in this area include: Neural Feature Geometry Evolves as Discrete Ricci Flow, which introduces a novel framework for understanding neural feature geometry through the lens of discrete geometry. LEAP: Local ECT-Based Learnable Positional Encodings for Graphs, which proposes a new end-to-end trainable local structural positional encoding for graphs. Equivariant Geometric Scattering Networks via Vector Diffusion Wavelets, which introduces a novel version of the geometric scattering transform for geometric graphs containing scalar and vector node features.

Sources

Cycle is All You Need: More Is Different

Exact Subgraph Isomorphism Network for Predictive Graph Mining

Neural Feature Geometry Evolves as Discrete Ricci Flow

NeuSO: Neural Optimizer for Subgraph Queries

VNODE: A Piecewise Continuous Volterra Neural Network

Well-Quasi-Ordering Eulerian Digraphs Embeddable in Surfaces by Strong Immersion

Graph2Region: Efficient Graph Similarity Learning with Structure and Scale Restoration

Hierarchy-Aware Neural Subgraph Matching with Enhanced Similarity Measure

LEAP: Local ECT-Based Learnable Positional Encodings for Graphs

Equivariant Geometric Scattering Networks via Vector Diffusion Wavelets

Built with on top of