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

Autor:	Nauck, Christian, Gorantla, Rohan, Lindner, Michael, Schürholt, Konstantin, Mey, Antonia S. J. S., Hellmann, Frank
Rok vydání:	2024
Předmět:	Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.12419 Zobrazit plný text záznamu View this record from Arxiv