将连续时间图网络拓展到非欧几何空间，提升复杂图结构建模能力
Riemannian Liquid Spatio-Temporal Graph Network
- 在黎曼流形上构建连续时间图神经网络，融合几何先验
- 在真实数据集上实现更优的时空图建模性能
- 适合处理具有层次、循环等复杂结构的动态图数据
液态时间常数网络（LTC）是一种连续时间图神经网络，擅长建模不规则采样动态，但其固有局限在于仅适用于欧氏空间。当处理具有内在非欧几何时序结构（如层次结构和环路）的真实图时，这种限制会引入显著的几何失真，降低表示质量。为克服此问题，本文提出黎曼液态时空图网络（RLSTG），该框架将连续时间液态动力学与黎曼流形的几何归纳偏置相统一。RLSTG通过直接定义在弯曲流形上的常微分方程（ODE）来建模图演化，能够忠实捕捉静态与动态时空图的内在几何特性。此外，本文提供了严格的理论保证，将LTC的稳定性定理推广至黎曼域，并通过状态轨迹分析量化了模型表达能力。在多个真实世界基准测试中的大量实验表明，结合先进时序动态与黎曼空间表示，RLSTG在复杂结构图上实现了卓越性能。
原文摘要 · Abstract (English)
Liquid Time-Constant networks (LTCs), a type of continuous-time graph neural network, excel at modeling irregularly-sampled dynamics but are fundamentally confined to Euclidean space. This limitation introduces significant geometric distortion when representing real-world graphs with inherent non-Euclidean structures (e.g., hierarchies and cycles), degrading representation quality. To overcome this limitation, we introduce the Riemannian Liquid Spatio-Temporal Graph Network (RLSTG), a framework that unifies continuous-time liquid dynamics with the geometric inductive biases of Riemannian manifolds. RLSTG models graph evolution through an Ordinary Differential Equation (ODE) formulated directly on a curved manifold, enabling it to faithfully capture the intrinsic geometry of both structurally static and dynamic spatio-temporal graphs. Moreover, we provide rigorous theoretical guarantees for RLSTG, extending stability theorems of LTCs to the Riemannian domain and quantifying its expressive power via state trajectory analysis. Extensive experiments on real-world benchmarks demonstrate that, by combining advanced temporal dynamics with a Riemannian spatial representation, RLSTG achieves superior performance on graphs with complex structures. Project Page: https://rlstg.github.io
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