Graph neural networks (GNN) have shown great advantages in many graph-based
learning tasks but often fail to predict accurately for a task-based on sets of
nodes such as link/motif prediction and so on. Many works have recently
proposed to address this problem by using random node features or node distance
features. However, they suffer from either slow convergence, inaccurate
prediction, or high complexity. In this work, we revisit GNNs that allow using
positional features of nodes given by positional encoding (PE) techniques such
as Laplacian Eigenmap, Deepwalk, etc. GNNs with PE often get criticized because
they are not generalizable to unseen graphs (inductive) or stable. Here, we
study these issues in a principled way and propose a provable solution, a class
of GNN layers termed PEG with rigorous mathematical analysis. PEG uses separate
channels to update the original node features and positional features. PEG
imposes permutation equivariance w.r.t. the original node features and imposes
$O(p)$ (orthogonal group) equivariance w.r.t. the positional features
simultaneously, where $p$ is the dimension of used positional features.
Extensive link prediction experiments over 8 real-world networks demonstrate
the advantages of PEG in generalization and scalability.

本文讨论了使用位置编码技术来改进图神经网络在节点集合任务中预测的问题，并提出了一种被称为 PEG 的类 GNN 层，它使用单独的通道更新原始节点特征和位置特征。PEG 同时对原始节点特征施加排列等变性质，并对位置特征施加 O（p）等变性质，其中 p 是使用的位置特征的维度。在 8 个真实世界网络上的广泛链接预测实验表明，PEG 在泛化和可伸缩性方面具有优势。