Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly, but suffer from high computational complexity and have to rely on ad-hoc positional encoding to bake in the graph inductive bias. In this paper, we propose a new architecture to reconcile these challenges. Our approach stems from the recent breakthroughs in long-range modeling provided by deep state-space models on sequential data: for a given target node, our model aggregates other nodes by their shortest distances to the target and uses a parallelizable linear recurrent network over the chain of distances to provide a natural encoding of its neighborhood structure. With no need for positional encoding, we empirically show that the performance of our model is highly competitive compared with that of state-of-the-art graph transformers on various benchmarks, at a drastically reduced computational complexity. In addition, we show that our model is theoretically more expressive than one-hop message passing neural networks.

翻译：基于迭代单跳消息传递的图神经网络已被证明难以有效利用来自远处节点的信息。相反，图Transformer允许每个节点直接关注所有其他节点，但存在计算复杂度高的问题，并且需要依赖专门的相对位置编码来融入图归纳偏置。本文提出了一种新架构来调和这些挑战。我们的方法源于近期深度状态空间模型在序列数据长程建模方面的突破：对于给定的目标节点，我们的模型根据其他节点到目标节点的最短距离进行聚合，并利用距离链上的可并行化线性递归网络提供邻域结构的自然编码。在无需位置编码的情况下，我们通过实验证明，该模型的性能与多个基准测试中的最先进图Transformer相比极具竞争力，同时计算复杂度大幅降低。此外，我们还证明该模型在理论上比单跳消息传递神经网络更具表达能力。