- Weisfeiler and Lehman Go Mobile: CW Networks
Authors: Cristian Bodnar, Fabrizio Frasca, Nina Otter, Yu Guang Wang, Pietro Liò, Guido Montúfar, Michael Bronstein
Summary: Graph Neural Networks (GNNs) are restricted of their expressive energy, battle with long-range interactions and lack a principled method to mannequin higher-order buildings. These issues may be attributed to the sturdy coupling between the computational graph and the enter graph construction. The just lately proposed Message Passing Simplicial Networks naturally decouple these components by performing message passing on the clique complicated of the graph. Nonetheless, these fashions may be severely constrained by the inflexible combinatorial construction of Simplicial Complexes (SCs). On this work, we lengthen latest theoretical outcomes on SCs to common Cell Complexes, topological objects that flexibly subsume SCs and graphs. We present that this generalisation gives a strong set of graph “lifting” transformations, every resulting in a novel hierarchical message passing process. The ensuing strategies, which we collectively name CW Networks (CWNs), are strictly extra highly effective than the WL take a look at and never much less highly effective than the 3-WL take a look at. Particularly, we show the effectiveness of 1 such scheme, based mostly on rings, when utilized to molecular graph issues. The proposed structure advantages from provably bigger expressivity than generally used GNNs, principled modelling of higher-order indicators and from compressing the distances between nodes. We show that our mannequin achieves state-of-the-art outcomes on a wide range of molecular datasets
