Riemannian Liquid Spatio-Temporal Graph Network

Authors

† Co-first author ✉ Corresponding author

Liangsi Lu † Guangdong University of Technology, Guangzhou, China
Jingchao Wang † Peking University, Beijing, China
Zhaorong Dai South China Agricultural University, Guangzhou, China
Hanqian Liu Sun Yat-Sen University, Guangzhou, China
Yang Shi ✉ Guangdong University of Technology, Guangzhou, China

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.

BibTeX

@misc{lu2026rlstg,
  title={Riemannian Liquid Spatio-Temporal Graph Network},
  author={Liangsi Lu and Jingchao Wang and Zhaorong Dai and Hanqian Liu and Yang Shi},
  year={2026},
  eprint={2601.14115},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2601.14115},
}