Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions

TL;DR

This paper introduces Dirac--Bianconi GNNs (DBGNNs), a novel architecture based on the topological Dirac equation, enabling non-diffusive, long-range graph predictions that outperform traditional message passing neural networks.

Contribution

The paper presents DBGNNs, a new GNN architecture inspired by the topological Dirac equation, offering a fundamentally different approach to exploring graph geometry and long-range information propagation.

Findings

DBGNNs outperform conventional MPNNs in long-range predictions.

Experimental results on power grid stability and peptide properties show superior accuracy.

DBGNNs explore graph geometry in a non-diffusive, coherent manner.

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.