Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes
This addresses graph expressivity limitations in machine learning, offering a novel approach for researchers and practitioners in graph-based tasks, though it builds on prior topological GNNs.
The paper tackles the limited expressivity of Graph Neural Networks (GNNs) by introducing a model that uses simple paths in graphs via path complexes, freeing it from assumptions about sub-structures like cliques or cycles, and achieves state-of-the-art results on various benchmarks.
Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on topological higher-order GNNs overcome that boundary, these models often depend on assumptions about sub-structures of graphs. Specifically, topological GNNs leverage the prevalence of cliques, cycles, and rings to enhance the message-passing procedure. Our study presents a novel perspective by focusing on simple paths within graphs during the topological message-passing process, thus liberating the model from restrictive inductive biases. We prove that by lifting graphs to path complexes, our model can generalize the existing works on topology while inheriting several theoretical results on simplicial complexes and regular cell complexes. Without making prior assumptions about graph sub-structures, our method outperforms earlier works in other topological domains and achieves state-of-the-art results on various benchmarks.