Weisfeiler and Lehman Go Cellular: CW Networks

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models can be severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higher-order signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification CSL CIN Acc 1 # 1
Graph Property Prediction ogbg-molhiv CIN Test ROC-AUC 0.8094 ± 0.0057 # 10
Validation ROC-AUC 0.8277 ± 0.0099 # 22
Number of params 239745 # 29
Ext. data No # 1
Graph Property Prediction ogbg-molhiv CIN-small Test ROC-AUC 0.8055 ± 0.0104 # 14
Validation ROC-AUC 0.8310 ± 0.0102 # 18
Number of params 138337 # 32
Ext. data No # 1
Graph Regression ZINC CIN-small MAE 0.094 # 14
Graph Regression ZINC CIN MAE 0.079 # 11
Graph Regression ZINC 100k CIN-small MAE 0.094 # 1
Graph Regression ZINC-500k CIN MAE 0.079 # 9
Graph Regression ZINC-500k CIN-small MAE 0.094 # 13


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