Torsion Graph Neural Networks.

Area of Science:

• Graph Neural Networks (GNNs)
• Geometric Deep Learning (GDL)
• Topological Data Analysis

Background:

• Geometric deep learning models excel at analyzing non-Euclidean data by integrating geometric and topological information.
• Discrete Ricci curvature has shown success in enhancing Graph Neural Networks (GNNs).
• Characterizing local graph structures effectively is crucial for improving GNN performance.

Purpose of the Study:

• To propose TorGNN, a novel analytic Torsion enhanced Graph Neural Network model.
• To leverage analytic torsion as a topological invariant for characterizing graph local structures.
• To improve the performance of GNNs in link prediction and node classification tasks.

Main Methods:

• Developed TorGNN, a Graph Neural Network model incorporating analytic torsion.
• Characterized local graph structures using an analytic torsion-based weight formula for edges.
• Calculated analytic torsion for local simplicial complexes associated with each edge to weight the message-passing process.

Main Results:

• TorGNN demonstrated superior performance on link prediction tasks across sixteen diverse networks.
• TorGNN achieved state-of-the-art results on node classification tasks across four network types.
• The model consistently outperformed existing state-of-the-art GNN models.

Conclusions:

• Analytic torsion is a highly effective topological invariant for characterizing graph structures.
• Incorporating analytic torsion significantly enhances the performance of Graph Neural Networks.
• TorGNN represents a significant advancement in applying topological invariants to GNNs for improved data analysis.