Graph neural networks (GNNs) have achieved remarkable performance in a variety of graph-related tasks. Recent evidence in the GNN community shows that such good performance can be attributed to the homophily prior; i.e., connected nodes tend to have similar features and labels. However, in heterophilic settings where the features of connected nodes may vary significantly, GNN models exhibit notable performance deterioration. In this work, we formulate this problem as prior-data conflict and propose a model called the mixture-prior graph neural network (MPGNN). First, to address the mismatch of homophily prior on heterophilic graphs, we introduce the non-informative prior, which makes no assumptions about the relationship between connected nodes and learns such relationship from the data. Second, to avoid performance degradation on homophilic graphs, we implement a soft switch to balance the effects of homophily prior and non-informative prior by learnable weights. We evaluate the performance of MPGNN on both synthetic and real-world graphs. Results show that MPGNN can effectively capture the relationship between connected nodes, while the soft switch helps select a suitable prior according to the graph characteristics. With these two designs, MPGNN outperforms state-of-the-art methods on heterophilic graphs without sacrificing performance on homophilic graphs.

图神经网络（GNN）在各种与图相关的任务中取得了显着的性能。 GNN 社区的最新证据表明，如此好的性能可以归因于同质先验；即，连接的节点往往具有相似的特征和标签。然而，在异质环境中，连接节点的特征可能显着变化，GNN 模型表现出显着的性能恶化。在这项工作中，我们将此问题表述为先验数据冲突，并提出了一种称为混合先验图神经网络（MPGNN）的模型。首先，为了解决异亲图上同质先验的不匹配问题，我们引入了非信息先验，它不对连接节点之间的关系做出假设并从数据中学习这种关系。其次，为了避免同质图的性能下降，我们实现了一个软切换，通过可学习的权重来平衡同质先验和非信息先验的影响。我们评估 MPGNN 在合成图和真实世界图上的性能。结果表明，MPGNN 可以有效捕获连接节点之间的关系，而软切换有助于根据图的特征选择合适的先验。通过这两种设计，MPGNN 在异亲图上的性能优于最先进的方法，而不会牺牲在同亲图上的性能。