AI 中文总结
本研究提出一种基于残差推送的高效动态算法，用于在边插入和删除下维护非线性GNN传播的近似不动点，实现均摊$O(1/\epsilon)$更新时间，并在基准上验证了其准确性与高效性。
AI 中文摘要
图神经网络（GNN）被广泛用于图上的表示学习，但大多数方法假设静态拓扑，这使得它们在边随时间变化的演化网络上效率低下。现有的动态方法要么通过时间GNN架构对图演化进行建模，而不关注高效的动态维护，要么局限于基于个性化PageRank的线性传播模型。在这项工作中，我们研究了如何在边插入和删除的情况下高效维护非线性GNN传播的节点表示。该传播没有可学习参数，仅随后应用一个分类器进行训练。对于一大类标准激活函数，我们开发了一种基于残差的动态算法，通过推送操作选择性地传播局部误差，在不完全重新计算的情况下维护演化不动点的近似。我们证明，在度归一化误差保证下，我们的方法实现了每次图变化的均摊$O(1/\epsilon)$更新时间。我们的方法使用度缩放范数中的基于势的分析，并且与先前关于线性情况的工作相比，不需要对更新序列或输入向量做随机性假设。对于线性特例，我们还通过低秩矩阵逆更新提供了一种精确的动态算法。在基准数据集上的实验表明，引入非线性在保持高效更新性能的同时提高了准确性，为在动态图上维护这种传播提供了一种可扩展且具有理论依据的方法。
英文摘要
Graph Neural Networks (GNNs) are widely used for representation learning on graphs, but most methods assume static topologies, making them inefficient on evolving networks where edges change over time. Existing dynamic approaches either model graph evolution through temporal GNN architectures without focusing on efficient dynamic maintenance, or are restricted to linear propagation models based on Personalized PageRank. In this work, we study how to efficiently maintain node representations for non-linear GNN propagation under edge insertions and deletions. The propagation has no learned parameters, and only a classifier applied afterward is trained. For a broad class of standard activation functions, we develop a residual-based dynamic algorithm that selectively propagates local errors via push operations, maintaining an approximation to the evolving fixed point without full recomputation. We prove that our method achieves amortized $O(1/ε)$ update time per graph change under a degree-normalized error guarantee. Our approach uses a potential-based analysis in a degree-scaled norm and, in contrast to prior work on the linear case, requires no randomness assumptions on either the update sequence or the input vector. For the linear special case, we additionally provide an exact dynamic algorithm via low-rank matrix inverse updates. Experiments on benchmark datasets show that incorporating non-linearity improves accuracy while preserving efficient update performance, yielding a scalable and theoretically grounded method for maintaining this propagation on dynamic graphs.
CommentsAccepted at NeurIPS 2026
