It is by now a well known fact in the graph learning community that the presence of bottlenecks severely limits the ability of graph neural networks to propagate information over long distances. What so far has not been appreciated is that, counter-intuitively, also the presence of strongly connected sub-graphs may severely restrict information flow in common architectures. Motivated by this observation, we introduce the concept of multi-scale consistency. At the node level this concept refers to the retention of a connected propagation graph even if connectivity varies over a given graph. At the graph-level, multi-scale consistency refers to the fact that distinct graphs describing the same object at different resolutions should be assigned similar feature vectors. As we show, both properties are not satisfied by poular graph neural network architectures. To remedy these shortcomings, we introduce ResolvNet, a flexible graph neural network based on the mathematical concept of resolvents. We rigorously establish its multi-scale consistency theoretically and verify it in extensive experiments on real world data: Here networks based on this ResolvNet architecture prove expressive; out-performing baselines significantly on many tasks; in- and outside the multi-scale setting.

图学习中的瓶颈问题限制了图神经网络在长距离传播信息的能力，而本文提出了多尺度一致性的概念，并引入基于渐近算子的灵活图神经网络ResolvNet来解决这些问题。通过理论上的严格论证和大量实验验证，ResolvNet在真实世界数据上显示出了表达能力，显著超越了许多任务在多尺度环境内外的基准线。

ResolvNet: 一个具有多尺度一致性的图卷积网络