Real-world graphs grow rapidly with edge and vertex insertions over time, motivating the problem of efficiently maintaining robust node representation over evolving graphs. Recent efficient GNNs are designed to decouple recursive message passing from the learning process, and favor Personalized PageRank (PPR) as the underlying feature propagation mechanism. However, most PPR-based GNNs are designed for static graphs, and efficient PPR maintenance remains as an open problem. Further, there is surprisingly little theoretical justification for the choice of PPR, despite its impressive empirical performance. In this paper, we are inspired by the recent PPR formulation as an explicit $\ell_1$-regularized optimization problem and propose a unified dynamic graph learning framework based on sparse node-wise attention. We also present a set of desired properties to justify the choice of PPR in STOA GNNs, and serves as the guideline for future node attention designs. Meanwhile, we take advantage of the PPR-equivalent optimization formulation and employ the proximal gradient method (ISTA) to improve the efficiency of PPR-based GNNs upto 6 times. Finally, we instantiate a simple-yet-effective model (\textsc{GoPPE}) with robust positional encodings by maximizing PPR previously used as attention. The model performs comparably to or better than the STOA baselines and greatly outperforms when the initial node attributes are noisy during graph evolution, demonstrating the effectiveness and robustness of \textsc{GoPPE}.

本研究解决了动态图中保持鲁棒节点表示的效率问题，针对现有PPR（个性化页面排名）方法在静态图中的局限性，提出了一种基于稀疏节点注意力的统一动态图学习框架。研究表明，所提出的模型\textsc{GoPPE}在节点属性噪声明显时，具备优越的性能和稳健性，显著提高了PPR基于GNN的效率。

快速且稳健的动态图上下文节点表示学习