Spatial-Temporal Graph (STG) data is characterized as dynamic, heterogenous,
and non-stationary, leading to the continuous challenge of spatial-temporal
graph learning. In the past few years, various GNN-based methods have been
proposed to solely focus on mimicking the relationships among node individuals
of the STG network, ignoring the significance of modeling the intrinsic
features that exist in STG system over time. In contrast, modern Selective
State Space Models (SSSMs) present a new approach which treat STG Network as a
system, and meticulously explore the STG system's dynamic state evolution
across temporal dimension. In this work, we introduce Spatial-Temporal Graph
Mamba (STG-Mamba) as the first exploration of leveraging the powerful selective
state space models for STG learning by treating STG Network as a system, and
employing the Graph Selective State Space Block (GS3B) to precisely
characterize the dynamic evolution of STG networks. STG-Mamba is formulated as
an Encoder-Decoder architecture, which takes GS3B as the basic module, for
efficient sequential data modeling. Furthermore, to strengthen GNN's ability of
modeling STG data under the setting of SSSMs, we propose Kalman Filtering Graph
Neural Networks (KFGN) for adaptive graph structure upgrading. KFGN smoothly
fits in the context of selective state space evolution, and at the same time
keeps linear complexity. Extensive empirical studies are conducted on three
benchmark STG forecasting datasets, demonstrating the performance superiority
and computational efficiency of STG-Mamba. It not only surpasses existing
state-of-the-art methods in terms of STG forecasting performance, but also
effectively alleviate the computational bottleneck of large-scale graph
networks in reducing the computational cost of FLOPs and test inference time.

基于选择性状态空间模型，该研究提出了一种名为 STG-Mamba 的时空图学习方法，借助图选择性状态空间块（GS3B）刻画了 STG 网络的动态演化，并引入了 Kalman 滤波图神经网络（KFGN）来提升 GNN 在 STG 数据建模中的能力。大量实证研究表明了 STG-Mamba 在预测性能和计算效率方面的优越性。