The Logic of Graph Neural Networks

TL;DR

This paper explains the theoretical foundations of graph neural networks (GNNs), linking their expressiveness to Weisfeiler-Leman algorithms and finite variable logics, and discusses higher-order GNNs.

Contribution

It provides a detailed explanation of the descriptive characterisations of GNNs, connecting them to combinatorial algorithms and logical frameworks.

Findings

GNNs' expressiveness is characterized by Weisfeiler-Leman algorithms.

Higher-order GNNs correspond to higher-dimensional WL algorithms.

The paper clarifies the theoretical underpinnings of GNN expressiveness.

Abstract

Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics. The correspondence has even led to new, higher-order GNNs corresponding to the WL algorithm in higher dimensions. The purpose of this paper is to explain these descriptive characterisations of GNNs.