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

Authors
/persons/resource/nauck

Nauck,  Christian
Potsdam Institute for Climate Impact Research;

Gorantla,  Rohan
External Organizations;

/persons/resource/Michael.Lindner

Lindner,  Michael
Potsdam Institute for Climate Impact Research;

Schürholt,  Konstantin
External Organizations;

Mey,  Antonia S. J. S.
External Organizations;

/persons/resource/frank.hellmann

Hellmann,  Frank
Potsdam Institute for Climate Impact Research;

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Nauck_DBGNN-16.pdf
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Citation

Nauck, C., Gorantla, R., Lindner, M., Schürholt, K., Mey, A. S. J. S., Hellmann, F. (2024): Dirac-Bianconi Graph Neural Networks - Enabling Non-Diffusive Long-Range Graph Predictions, (Proceedings of Machine Learning Research ; 251).


Cite as: https://publications.pik-potsdam.de/pubman/item/item_30045
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.