Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

翻译：消息传递神经网络（MPNNs）已被证明存在过度挤压现象，导致依赖长程交互的任务性能较差。这很大程度上源于消息传递仅在局部进行（即节点的直接邻居之间）。试图使图“更具连通性”并以此更好地适应长程任务的重连方法，往往因让远距离节点在每一层即时通信而丧失图距离带来的归纳偏置。本文提出一个适用于任意MPNN架构的框架：通过层依赖的重连实现图的渐进式稠密化。我们还提出一种延迟机制，允许节点根据其层数及相互距离建立跳跃连接。我们在多个长程任务上验证了该方法，结果表明其性能优于图Transformer和多跳MPNN。