Riemannian Liquid Spatio-Temporal Graph Network
This work addresses the problem of modeling irregularly-sampled dynamics on non-Euclidean graphs for researchers in graph neural networks and spatio-temporal analysis, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackled the limitation of Liquid Time-Constant networks being confined to Euclidean space, which causes geometric distortion for non-Euclidean graphs, by introducing the Riemannian Liquid Spatio-Temporal Graph Network (RLSTG) that unifies continuous-time dynamics with Riemannian manifolds, achieving superior performance on real-world benchmarks with complex structures.
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