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.

本篇研究提出了基于 CW 网络的一种消息传递方法，将 Simplicial Complexes 扩展为适应更加灵活的 Cell Complexes，并在分子图问题上证明了该模型优越性。