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

TL;DR

This paper reevaluates the effectiveness of curvature-based graph rewiring in GNNs on real-world datasets, revealing that observed accuracy improvements are often due to hyperparameter tuning rather than genuine structural benefits.

Contribution

It critically assesses curvature-based rewiring, showing it may not improve GNN performance on real data and that hyperparameter tuning often explains observed gains.

Findings

Rewiring edges do not align with theoretical bottleneck criteria in real datasets.

State-of-the-art performance often results from hyperparameter sweeps, not structural improvements.

Curvature-based rewiring's effectiveness is less clear in real-world scenarios.

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.