Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

翻译：为提升图神经网络（GNN）性能，学界已探索出两类主要的节点特征增强方案：随机特征与谱位置编码。然而令人意外的是，这两类增强方案之间的关联至今仍未得到清晰阐释。本文提出一种新型位置编码方案族，该方案既架起了上述两类方法的桥梁，又在性能上实现了对二者的超越。这项名为"随机特征传播"（RFP）的新方法受乘幂法及其泛化形式启发，通过从随机节点特征出发，迭代计算传播矩阵主特征向量的中间步骤并将这些步骤进行串联。值得注意的是，这些传播步骤基于图依赖的传播算子，该算子既可预定义也可通过学习获得。我们从理论与实证两个维度探究了RFP的优势。首先，为采用随机特征、引入早期传播步骤以及使用多重随机初始化提供了理论依据。随后通过实验证明，在多项节点分类与图分类基准测试中，RFP的性能显著超越谱PE与随机特征。