Towards Expressive Graph Representation

TL;DR

This paper introduces an expressive GNN framework using continuous injective set functions for neighborhood aggregation, significantly enhancing graph representation capabilities and achieving state-of-the-art results on benchmarks.

Contribution

It proposes a novel theoretical framework for designing injective neighborhood aggregation functions, improving GNN expressiveness and performance.

Findings

Achieves state-of-the-art results on multiple graph classification benchmarks.

Effectively handles graphs with continuous node attributes.

Provides a theoretical basis for more expressive GNN design.

Abstract

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.