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：两类主要的节点特征增强方案已被探索用于提升图神经网络（GNN）：随机特征与频谱位置编码。然而令人惊讶的是，这两种增强方案之间的关系至今仍缺乏清晰理解。本文提出一类新颖的位置编码方案，该方案在建立两者联系的同时优于现有方法。这种名为随机特征传播（RFP）的新方法受幂迭代法及其推广形式的启发，它从随机节点特征出发，将计算传播矩阵主特征向量的迭代算法中的多个中间步骤进行拼接。值得注意的是，这些传播步骤基于可预定义或可学习的图依赖传播算子。我们从理论与实证两个层面探索RFP的优势：首先，为随机特征的采用、早期传播步骤的整合以及多重随机初始化的使用提供了理论依据；其次，通过实验证明，RFP在多个节点分类和图分类基准测试中显著优于频谱位置编码和随机特征。