Curvature MPNNs : Improving Message Passing with Local Structural Properties

Hugo Attali, Davide Buscaldi, Nathalie Pernelle

Primary Area: learning on graphs and other geometries & topologies

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Keywords: graph representation learning, oversquashing, graph rewiring, graph neural networks, curvature

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Abstract:

Graph neural networks follow an iterative scheme of updating node representations based on the aggregation from nearby nodes know as the message passing paradigm. Although they are widely used, it has been established that they suffer from a problem of oversquashing that limit their efficiency. Recently, it has been shown that the bottleneck phenomenon comes from certain areas of the graphs, which can be identified by a measure of edge curvature.
In this paper we propose a framework appropriate for any MPNN architecture called Curvature Message Passing, that distributes information based on the curvature of the graph's edges.
Experiments conducted on different datasets show that our method mitigate oversquashing and outperforms existing graph rewiring in several nodes classification tasks.

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Submission Number: 3493