Weisfeiler and Leman go Machine Learning: The Story so far

TL;DR

This paper reviews the integration of the Weisfeiler--Leman algorithm into machine learning, highlighting its theoretical foundations, recent extensions, and applications in graph and node representation learning.

Contribution

It provides a comprehensive overview of how Weisfeiler--Leman algorithms are used in supervised graph learning and their connection to neural architectures.

Findings

Theoretical insights into Weisfeiler--Leman's role in graph neural networks

Extensions of the algorithm for improved learning tasks

Current applications and future research directions

Abstract

In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine-learning setting, focusing on the supervised regime. We discuss the theoretical background, show how to use it for supervised graph and node representation learning, discuss recent extensions, and outline the algorithm's connection to (permutation-)equivariant neural architectures. Moreover, we give an overview of current applications and future directions to stimulate further research.