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）已被证明存在过压缩现象，这导致其在依赖长程交互的任务中性能欠佳。这一现象主要归因于消息传递仅局限于节点紧邻的局部范围内。旨在增强图"连通性"、并被认为更适用于长程任务的重连方法，往往因使远距离节点在每个网络层立即通信而丧失图距离提供的归纳偏置。本文提出一种适用于任意MPNN架构的框架，通过逐层依赖的重连策略确保图结构逐步稠密化。同时引入延迟机制，根据网络层与节点间的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，实验表明其性能优于图Transformer和多跳MPNN。