In the context of machine learning for graphs, many researchers have empirically observed that Deep Graph Networks (DGNs) perform favourably on node classification tasks when the graph structure is homophilic (\ie adjacent nodes are similar). In this paper, we introduce Lying-GCN, a new DGN inspired by opinion dynamics that can adaptively work in both the heterophilic and the homophilic setting. At each layer, each agent (node) shares its own opinions (node embeddings) with its neighbours. Instead of sharing its opinion directly as in GCN, we introduce a mechanism which allows agents to lie. Such a mechanism is adaptive, thus the agents learn how and when to lie according to the task that should be solved. We provide a characterisation of our proposal in terms of dynamical systems, by studying the spectral property of the coefficient matrix of the system. While the steady state of the system collapses to zero, we believe the lying mechanism is still usable to solve node classification tasks. We empirically prove our belief on both synthetic and real-world datasets, by showing that the lying mechanism allows to increase the performances in the heterophilic setting without harming the results in the homophilic one.

翻译：在图机器学习的背景下，许多研究者通过实验观察到，当图结构具有同质性（即相邻节点相似）时，深度图网络在节点分类任务上表现良好。本文提出Lying-GCN——一种受观点动力学启发的新深度图网络，能够自适应地在异质性和同质性场景下工作。在每一层中，每个智能体（节点）与邻居共享其自身观点（节点嵌入）。不同于图卷积网络中直接共享观点，我们引入了一种允许智能体谎报信息的机制。该机制具有自适应性，智能体可根据待解决的任务学习如何及何时说谎。我们从动力系统角度对方法进行刻画，通过研究系统系数矩阵的谱性质。尽管系统稳态会坍缩至零，但我们认为该谎报机制仍可用于解决节点分类任务。通过在合成数据集和真实数据集上的实验证明，该谎报机制能在不影响同质性场景性能的前提下，提升异质性场景的表现。