Scaling Higher-Order Graph Learning with Maximal Clique Complexes

2026-05-29

AI Summary

Existing graph neural networks struggle to model higher-order interactions, while approaches based on cellular complexes offer strong expressivity but suffer from poor scalability. This work proposes an efficient and scalable framework for higher-order graph learning by introducing simplified and factorized variants of the cellular Weisfeiler–Leman (sCWL/fCWL) test, which substantially improve computational efficiency without sacrificing expressiveness. To avoid explicit clique enumeration, the method leverages a maximal-clique complex and designs CliqueWalk—a linear-complexity sampling strategy combined with biased random walks for effective neighborhood exploration. Building upon this foundation, the authors develop Cellular Message Passing Networks (CWNs), achieving time and memory complexity linear in the graph size while maintaining state-of-the-art performance across multiple benchmarks.

Abstract

Graph neural networks (GNNs) are limited to modeling pairwise interactions, while higher-order models based on cell complexes achieve greater expressivity but often suffer from poor scalability. We introduce simplified and factored cellular Weisfeiler Leman tests (sCWL and fCWL), which preserve the expressivity of the CWL test while improving computational efficiency. We further introduce the maximal clique complex, enabling scalable CWNs with reduced time and memory complexity while retaining strong empirical performance. To avoid explicit clique enumeration, we propose CliqueWalk, a biased random walk that samples maximal cliques and scales linearly with graph size. These contributions yield a scalable topological learning framework for higher-order graph representation.

Problem

• higher-order graph learning
• graph neural networks
• cell complexes
• scalability
• maximal cliques

Innovation

• maximal clique complex
• cellular Weisfeiler-Leman
• CliqueWalk
• higher-order graph learning
• scalable topological learning