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 are 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, in certain cases, 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.
翻译:神经网络(GNNs)的表达力有限,与长距离互动抗争,缺乏建模高阶结构的原则性方法。这些问题可归因于计算图和输入图结构之间的强烈结合。最近提议的“传递信息的简化网络”自然地通过在图形的球状复杂部分传递信息而使这些元素相交。然而,这些模型受到Simplicial Complex(SCs)的僵硬组合结构的严格限制。在这项工作中,我们把有关SC的最近理论结果推广到常规细胞综合体,以及灵活地在SC和图表中进行子化的表层物体。我们表明,这种概括提供了一套强有力的图表“提升”的变形图,每个变式都会导致独特的等级传递信息程序。由此产生的方法(我们统称为 CW 网络(CN) ), 严格来说比WL 测试更强大, 在某些情况下, 并不比 3WL 测试更强大。特别是, 我们展示了一种基于星环的理论的有效性, 其基础是, 当应用到分子分子型模型的更高级的模型, 我们使用的模型中度的模型, 的模型无法从共同的模型显示我们使用的模型的模型的模型的模型中, 。 结构的模型从我们使用的模型的模型的模型的模型中, 获得的模型的效益。