Papers › Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes
Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes
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
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| 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 |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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