Building powerful and equivariant graph neural networks with structural message-passing

TL;DR

This paper introduces a novel equivariant message-passing framework for graph neural networks that enhances representation power by incorporating local topological information and ensures permutation equivariance, leading to improved topological property prediction and molecular regression performance.

Contribution

It proposes a new message-passing approach that propagates node one-hot encodings to capture local topology and designs permutation-equivariant functions for better generalization.

Findings

Outperforms previous methods in predicting graph topological properties on synthetic data.

Achieves state-of-the-art results on molecular graph regression on the ZINC dataset.

Enhances representation power and generalization of graph neural networks.

Abstract

Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures in order to achieve good generalization. However, current message-passing architectures have a limited representation power and fail to learn basic topological properties of graphs. We address this problem and propose a powerful and equivariant message-passing framework based on two ideas: first, we propagate a one-hot encoding of the nodes, in addition to the features, in order to learn a local context matrix around each node. This matrix contains rich local information about both features and topology and can eventually be pooled to build node representations. Second, we propose methods for the parametrization of the message and update functions that ensure permutation equivariance. Having a representation that is independent of the specific choice of the one-hot encoding permits inductive reasoning and leads to better generalization properties. Experimentally, our model can predict various graph topological properties on synthetic data more accurately than previous methods and achieves state-of-the-art results on molecular graph regression on the ZINC dataset.