提出可置换等变的图神经微分方程，提升动态图建模效率与泛化能力。
Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning
- 将图神经微分方程投影到置换等变函数空间，降低参数量。
- 在模拟与真实数据上均实现插值和外推性能提升。
- 适合需要高效动态图建模的场景，如交通预测、社交网络分析。
动态图因节点特征与网络结构的协同演化而表现出复杂的时序动态。近期，图神经微分方程（Graph Neural CDEs）成功将神经微分方程从欧几里得域路径推广至图域路径。在此基础上，本文提出置换等变图神经微分方程（Permutation Equivariant Neural Graph CDEs），将图神经微分方程投影至置换等变函数空间。该方法显著减少模型参数量，同时保持表示能力，实现更高效的训练与更强的泛化性能。通过在模拟动力系统与真实任务上的实验验证，所提方法在插值与外推场景中均取得更优表现。
原文摘要 · Abstract (English)
Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce Permutation Equivariant Neural Graph CDEs, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios.
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