How Powerful are Graph Neural Networks?

TL;DR

This paper provides a theoretical analysis of the expressive power of Graph Neural Networks (GNNs), revealing their limitations, and introduces a new architecture that is provably the most expressive, matching the Weisfeiler-Lehman test, with empirical validation on benchmarks.

Contribution

It offers a theoretical framework for GNN expressiveness, identifies limitations of existing variants, and proposes a new, maximally expressive GNN architecture with state-of-the-art results.

Findings

Existing GNN variants cannot distinguish certain simple graph structures.

The proposed architecture is as powerful as the Weisfeiler-Lehman test.

The new GNN achieves state-of-the-art performance on benchmarks.

Abstract

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.