Deep Graph Predictions using Dirac-Bianconi Graph Neural Networks
Primary Area: learning on graphs and other geometries & topologies
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Keywords: Graph Neural Networks, graph convolution, physic inspired machine learning
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TL;DR: Dirac-Bianconi graph operator inspired graph neural network layer enables deep predictions of GNNs overcoming oversmoothing
Abstract: Viewing Graph Neural Networks as network dynamical systems on graphs has proven a fruitful inspiration for designing interesting GNN architectures. This work introduces the Dirac-Bianconi Graph Neural Network (DBGNN) based on Bianconi's topological Dirac equation on graphs. While heat equations based on network Laplacian tend to smooth out differences, Dirac equations typically feature long-range propagation. We indeed find that the DBGNN layer does not lead to an equilibration, or smoothing, of nodal features, even after hundreds of steps. A further distinguishing feature of the topological Dirac equation is that it treats edges and nodes on the same footing. Consequently, we expect DBGNN to be useful in contexts where edges encode more than mere logical connectivity, but have physical properties as well. We show competitive performance for molecular property prediction and superior performance for predicting the dynamic stability of power grids. In the case of power grids, DBGNN achieves robust out-of-distribution generalization, showing that structural relations are learned.
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Submission Number: 4015
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