Breaking the Expression Bottleneck of Graph Neural Networks

Abstract

Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressiveness of graph neural networks (GNNs), showing that the neighborhood aggregation GNNs were at most as powerful as 1-WL test in distinguishing graph structures. There were also improvements proposed in analogy to k-WL test ( <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$k&gt;1$</tex></formula> ). However, the aggregations in these GNNs are far from injective as required by the WL test, and suffer from weak distinguishing strength, making it become the expression bottleneck. In this paper, we improve the expressiveness by exploring powerful aggregations. We reformulate an aggregation with the corresponding aggregation coefficient matrix, and then systematically analyze the requirements on this matrix for building more powerful and even injective aggregations. We also show the necessity of applying nonlinear units ahead of aggregations, which is different from most existing GNNs. Based on our theoretical analysis, we develop ExpandingConv. Experimental results show that our model significantly boosts performance, especially for large and densely connected graphs.