Affinity-Aware Graph Networks

TL;DR

This paper introduces affinity-aware features based on random walk measures into graph neural networks, enhancing their expressivity and performance on various graph tasks with fewer message passing steps.

Contribution

It proposes a novel message passing network that incorporates affinity measures like effective resistance and commute times, improving efficiency and accuracy.

Findings

Achieved state-of-the-art validation MAE on OGB-LSC-PCQM4Mv1 dataset.

Outperformed benchmarks on multiple node and graph property prediction tasks.

Reduced computational complexity while maintaining high performance.

Abstract

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been significant interest in improving their expressivity by incorporating structural aspects of the underlying graph. In this paper, we explore the use of affinity measures as features in graph neural networks, in particular measures arising from random walks, including effective resistance, hitting and commute times. We propose message passing networks based on these features and evaluate their performance on a variety of node and graph property prediction tasks. Our architecture has lower computational complexity, while our features are invariant to the permutations of the underlying graph. The measures we compute allow the network to exploit the connectivity properties of the graph, thereby allowing us to outperform relevant benchmarks for a wide variety of tasks, often with significantly fewer message passing steps. On one of the largest publicly available graph regression datasets, OGB-LSC-PCQM4Mv1, we obtain the best known single-model validation MAE at the time of writing.