TY - GEN
T1 - Weisfeiler and Lehman Go Cellular
T2 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
AU - Bodnar, Cristian
AU - Frasca, Fabrizio
AU - Otter, Nina
AU - Wang, Yu Guang
AU - Liò, Pietro
AU - Montúfar, Guido
AU - Bronstein, Michael
N1 - Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85117764471&partnerID=8YFLogxK
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AN - SCOPUS:85117764471
T3 - Advances in Neural Information Processing Systems
SP - 2625
EP - 2640
BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
A2 - Ranzato, Marc'Aurelio
A2 - Beygelzimer, Alina
A2 - Dauphin, Yann
A2 - Liang, Percy S.
A2 - Wortman Vaughan, Jenn
PB - Neural information processing systems foundation
Y2 - 6 December 2021 through 14 December 2021
ER -