  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 Spatial-Temporal Selective State Space Module (ST-S3M) to
precisely focus on the selected STG latent features. Furthermore, to strengthen
GNN's ability of modeling STG data under the setting of selective state space
models, we propose Kalman Filtering Graph Neural Networks (KFGN) for
dynamically integrate and upgrade the STG embeddings from different temporal
granularities through a learnable Kalman Filtering statistical theory-based
approach. 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.
The implementation code is available at:
\url{https://github.com/LincanLi98/STG-Mamba}.
