Towards Expressive Graph Representation
This work addresses a fundamental limitation in graph representation learning for researchers and practitioners, though it is incremental as it builds on existing GNN methods.
The authors tackled the problem of limited expressiveness in Graph Neural Networks (GNNs) due to non-injective aggregation functions, proposing a theoretical framework for continuous injective set functions to improve node and graph embeddings, and demonstrated state-of-the-art performance on multiple benchmark datasets for graph classification.
Graph Neural Network (GNN) aggregates the neighborhood of each node into the node embedding and shows its powerful capability for graph representation learning. 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, reducing the model expressiveness. We present a theoretical framework to design a continuous injective set function for neighborhood aggregation in GNN. Using the framework, we propose expressive GNN that aggregates the neighborhood of each node with a continuous injective set function, so that a GNN layer maps similar nodes with similar neighborhoods to similar embeddings, different nodes to different embeddings and the equivalent nodes or isomorphic graphs to the same embeddings. Moreover, the proposed expressive GNN can naturally learn expressive representations for graphs with continuous node attributes. We validate the proposed expressive GNN (ExpGNN) for graph classification on multiple benchmark datasets including simple graphs and attributed graphs. The experimental results demonstrate that our model achieves state-of-the-art performances on most of the benchmarks.