Towards Expressive Graph Representations for Graph Neural Networks

Graph Neural Network (GNN) aggregates the neighborhood information into the node embedding and shows its powerful capability for graph representation learning in various application areas. However, most existing GNN variants aggregate the neighborhood information in a fixed non-injective fashion, which may map different graphs or nodes to the same embedding, detrimental to the model expressiveness. In this paper, we present a theoretical framework to improve the expressive power of GNN by taking both injectivity and continuity into account. Based on the framework, we develop injective and continuous expressive Graph Neural Network (iceGNN) that learns the graph and node representations in an injective and continuous fashion, so that it can map similar nodes or graphs to similar embeddings, and non-equivalent nodes or non-isomorphic graphs to different embeddings. We validate the proposed iceGNN model for graph classification and node classification on multiple benchmark datasets. The experimental results demonstrate that our model achieves state-of-the-art performances on most of the benchmarks.