Commute-Time-Optimised Graphs for GNNs
This work addresses graph rewiring for GNNs, but it appears incremental as it builds on existing commute-time-optimal methods by incorporating expert priors.
The paper tackles the problem of graph rewiring for Graph Neural Networks by proposing methods that optimize commute time between privileged node pairs when expert priors exist, demonstrating improved test performance on synthetic datasets with known priors and exploring practical implications in a real-world citation graph case study.
We explore graph rewiring methods that optimise commute time. Recent graph rewiring approaches facilitate long-range interactions in sparse graphs, making such rewirings commute-time-optimal on average. However, when an expert prior exists on which node pairs should or should not interact, a superior rewiring would favour short commute times between these privileged node pairs. We construct two synthetic datasets with known priors reflecting realistic settings, and use these to motivate two bespoke rewiring methods that incorporate the known prior. We investigate the regimes where our rewiring improves test performance on the synthetic datasets. Finally, we perform a case study on a real-world citation graph to investigate the practical implications of our work.