Going Deeper into Permutation-Sensitive Graph Neural Networks

TL;DR

This paper introduces a permutation-sensitive graph neural network that captures relationships among neighboring nodes, surpassing traditional invariant methods in expressivity and efficiency, with proven theoretical advantages and strong empirical results.

Contribution

We propose a novel permutation-sensitive aggregation mechanism for GNNs that is more expressive than 2-WL and as powerful as 3-WL, with linear sampling complexity.

Findings

Our method is strictly more powerful than 2-WL.

It is not less powerful than 3-WL.

Experiments show superior performance on synthetic and real datasets.

Abstract

The invariance to permutations of the adjacency matrix, i.e., graph isomorphism, is an overarching requirement for Graph Neural Networks (GNNs). Conventionally, this prerequisite can be satisfied by the invariant operations over node permutations when aggregating messages. However, such an invariant manner may ignore the relationships among neighboring nodes, thereby hindering the expressivity of GNNs. In this work, we devise an efficient permutation-sensitive aggregation mechanism via permutation groups, capturing pairwise correlations between neighboring nodes. We prove that our approach is strictly more powerful than the 2-dimensional Weisfeiler-Lehman (2-WL) graph isomorphism test and not less powerful than the 3-WL test. Moreover, we prove that our approach achieves the linear sampling complexity. Comprehensive experiments on multiple synthetic and real-world datasets demonstrate the superiority of our model.