Heterophily has been considered as an issue that hurts the performance of Graph Neural Networks (GNNs). To address this issue, some existing work uses a graph-level weighted fusion of the information of multi-hop neighbors to include more nodes with homophily. However, the heterophily might differ among nodes, which requires to consider the local topology. Motivated by it, we propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Moreover, we provide theoretical analysis on the effectiveness of LocalSim representing node homophily on synthetic graphs. Extensive evaluations over real benchmark datasets show that our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs. Meanwhile, the plug-and-play model can significantly boost the performance of existing GNNs. Our code is provided at https://github.com/draym28/LSGNN.

翻译：异质性（Heterophily）常被视为影响图神经网络（GNNs）性能的关键问题。针对该问题，现有工作多采用图级别的多跳邻居信息加权融合策略以纳入更多同质性节点。然而，异质性可能因节点而异，这要求必须考虑局部拓扑结构。受此启发，本文提出利用局部相似性（LocalSim）实现节点级别的加权融合，该模块可作为即插即用组件。为提升融合效果，我们设计了一种新颖高效的初始残差差分连接（IRDC）以提取更具信息量的多跳邻域特征。此外，我们在合成图上对LocalSim表征节点同质性的有效性进行了理论分析。在真实基准数据集上的广泛评估表明，所提方法——局部相似性图神经网络（LSGNN）——在同质性和异质性图的任务中均达到了可比或最优的先进性能。同时，该即插即用模型能够显著提升现有GNNs的性能。相关代码开源于https://github.com/draym28/LSGNN。