Papers › Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes

Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes

13 Aug 2023arXiv:2308.06838archive 2025-07-28

Quang Truong, Peter Chin

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.

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Tasks

Graph ClassificationGraph Property PredictionGraph Regression

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Graph Classification IMDb-B PIN Accuracy 76.6% #18 of 51 Archive leaderboard report
Graph Classification NCI1 PIN Accuracy 85.1% #15 of 69 Archive leaderboard report
Graph Classification NCI109 PIN Accuracy 84.0 #7 of 38 Archive leaderboard report
Graph Classification PROTEINS PIN Accuracy 78.8% #16 of 103 Archive leaderboard report
Graph Property Prediction ogbg-molhiv PIN Test ROC-AUC 0.7944 ± 1.40 #22 of 43 Archive leaderboard report
Graph Regression ZINC PIN MAE 0.096 #20 of 27 Archive leaderboard report

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