Title: Scaling Higher-Order Graph Learning with Maximal Clique Complexes
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Neural Networks, Topological Neural Networks, Random walks on cliques, Scalability, Cellular Neural Networks

Abstract: Graph neural networks (GNNs) are widely used for learning on graphs but are fundamentally limited to modeling pairwise relationships. 
Topological models, such as simplicial or cell complex networks, extend GNNs to higher-order structures and achieve stronger expressivity, but they suffer from severe scalability issues since they require learning over all possible cliques of a given size-a problem that becomes computationally infeasible on large graphs. In this paper, we study whether maximal cliques can be exploited efficiently for higher-order graph learning.  We introduce the maximal clique complex, a simplified higher-order structure that directly encodes maximal cliques of a graph, and show that a simplified cellular Weisfeiler network (sCWN) operating on this complex is as expressive as the full cellular Weisfeiler-Leman (CWL) test. To address scalability, we propose CliqueWalk, a biased random walk algorithm that samples cliques efficiently and scales quasi-linearly with the number of nodes. Building on these ideas, we design simplified clique-based neural architectures that preserve CWL-level expressivity while reducing computational and memory costs. Our models achieve competitive performance on both node and graph classification benchmarks, offering a scalable and theoretically grounded framework for higher-order graph learning.