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：为增强图神经网络（GNN）的性能，目前已探索了两种主要的节点特征增强方案：随机特征与频谱位置编码。然而令人意外的是，这两种增强方案之间的关联至今仍缺乏明确理解。本文提出一种新型位置编码方案族，该方案建立了上述两种方法的联系，并实现了对两者的性能改进。该方法名为随机特征传播（RFP），其灵感来源于幂迭代法及其推广形式。该方案将求解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，初始化为随机节点特征。值得注意的是，这些传播步骤基于可预定义或可学习的图相关传播算子。我们深入探究了RFP的理论与实证优势。首先，我们为随机特征的使用、早期传播步骤的整合以及多重随机初始化的运用提供了理论依据。随后，通过实证研究证明，在多个节点分类与图分类基准测试中，RFP的性能显著优于频谱位置编码与随机特征方案。