The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisited

Floriano Tori, Vincent Holst, Vincent Ginis

Keywords: Geometric deep learning, Graph Neural Networks, Graph Rewiring, Curvature

TL;DR: Our research challenges the effectiveness of curvature-based rewiring methods, revealing their dependence on hyperparameter tuning and questioning their applicability to real-world datasets.

Abstract: Message passing is the dominant paradigm in Graph Neural Networks (GNNs). The efficiency of message passing, however, can be limited by the topology of the graph. This happens when information is lost during propagation due to being oversquashed when travelling through bottlenecks. To remedy this, recent efforts have focused on graph rewiring techniques, which disconnect the input graph originating from the data and the computational graph, on which message passing is performed. A prominent approach for this is to use discrete graph curvature measures, of which several variants have been proposed, to identify and rewire around bottlenecks, facilitating information propagation. While oversquashing has been demonstrated in synthetic datasets, in this work we reevaluate the performance gains that curvature-based rewiring brings to real-world datasets. We show that in these datasets, edges selected during the rewiring process are not in line with theoretical criteria identifying bottlenecks. This implies they do not necessarily oversquash information during message passing. Subsequently, we demonstrate that SOTA accuracies on these datasets are outliers originating from sweeps of hyperparameters—both the ones for training and dedicated ones related to the rewiring algorithm—instead of consistent performance gains. In conclusion, our analysis nuances the effectiveness of curvature-based rewiring in real-world datasets and brings a new perspective on the methods to evaluate GNN accuracy improvements.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 10226