Dirac--Bianconi Graph Neural Networks - Enabling long-range graph predictions

Christian Nauck, Rohan Gorantla, Michael Lindner, Konstantin Schürholt, Antonia S J S Mey, Frank Hellmann

Track: Proceedings

Keywords: Graph Neural Networks, Long-range graph predictions

TL;DR: The paper introduces Dirac-Bianconi Graph Neural Networks (DBGNN), utilizing the topological Dirac equation for non-diffusive coherent long-range feature propagation on graphs, outperforming conventional message-passing networks in different tasks.

Abstract:

The geometry of a graph is encoded in dynamical processes on the graph. Many graph neural network (GNN) architectures are inspired by such dynamical systems, typically based on the graph Laplacian. Here, we introduce Dirac--Bianconi GNNs (DBGNNs), which are based on the topological Dirac equation recently proposed by Bianconi.
Based on the graph Laplacian, we demonstrate that DBGNNs explore the geometry of the graph in a fundamentally different way than conventional message passing neural networks (MPNNs).
While regular MPNNs propagate features diffusively, analogous to the heat equation, DBGNNs allow for coherent long-range propagation.
Experimental results showcase the superior performance of DBGNNs over existing conventional MPNNs for long-range predictions of power grid stability and peptide properties. This study highlights the effectiveness of DBGNNs in capturing intricate graph dynamics, providing notable advancements in GNN architectures.

Submission Number: 22