Riemannian Liquid Spatio-Temporal Graph Network

TL;DR

The paper introduces RLSTG, a Riemannian extension of liquid spatio-temporal graph networks, enabling better modeling of non-Euclidean graph structures with theoretical guarantees and superior real-world performance.

Contribution

It unifies continuous-time graph dynamics with Riemannian geometry, providing a novel framework that captures intrinsic graph structures more faithfully than Euclidean models.

Findings

RLSTG outperforms existing models on complex real-world benchmarks.

Theoretical stability and expressive power are rigorously established.

Model effectively captures non-Euclidean geometries in dynamic graphs.

Abstract

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