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

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).

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Item Permalink: https://publications.pik-potsdam.de/pubman/item/item_30045 Version Permalink: https://publications.pik-potsdam.de/pubman/item/item_30045_1
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https://openreview.net/forum?id=mZzE0xh1QW (Publisher version)
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https://doi.org/10.48550/arXiv.2407.12419 (Preprint)
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 Creators:
Nauck, Christian1, Author              
Gorantla, Rohan 2, Author
Lindner, Michael1, Author              
Schürholt, Konstantin 2, Author
Mey, Antonia S. J. S. 2, Author
Hellmann, Frank1, Author              
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1Potsdam Institute for Climate Impact Research, ou_persistent13              
2External Organizations, ou_persistent22              

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 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.

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Language(s): eng - English
 Dates: 2024-07-232024-06-182024-08-21
 Publication Status: Finally published
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 Rev. Type: Peer
 Identifiers: PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Working Group: Dynamics, stability and resilience of complex hybrid infrastructure networks
Research topic keyword: Energy
Model / method: Machine Learning
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Title: Proceedings of Machine Learning Research
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Pages: - Volume / Issue: 251 Sequence Number: - Start / End Page: - Identifier: -