How Powerful are Graph Neural Networks?
This work addresses a foundational gap in graph representation learning for researchers and practitioners by providing theoretical insights and a more expressive model, though it is incremental in building on existing GNN paradigms.
The paper tackled the limited understanding of Graph Neural Networks' (GNNs) representational power by developing a theoretical framework to analyze their ability to distinguish graph structures, showing that popular variants like Graph Convolutional Networks and GraphSAGE fail on certain simple structures, and proposing a new architecture that is provably as powerful as the Weisfeiler-Lehman test and achieves state-of-the-art performance on graph classification benchmarks.
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.