STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Model

TL;DR

This paper tackles forecasting for dynamic, non-stationary spatial-temporal graphs by proposing STG-Mamba, a selective state space modeling framework. It combines Kalman Filtering Graph Neural Networks (KFGN) for multi-temporal fusion with a Spatial-Temporal Selective State Space Module (ST-S3M) to perform input-dependent feature selection within a stacked GS3B encoder. The approach achieves linear-time complexity $O(L)$ and reduced FLOPs compared to Transformer-based methods, while delivering state-of-the-art forecasting performance on three real-world STG datasets. Empirical results demonstrate robustness across varying external conditions and clear ablations confirm the value of each component. This work provides a scalable, interpretable alternative to attention-based STG models for large-scale, real-world forecasting tasks.

Abstract

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}.

Figures (5)

• Figure 1: The comprehensive illustration of STG-Mamba's Model Architecture.
• Figure 2: Kalman Filtering Graph Neural Networks.
• Figure 3: Model component analysis of STG-Mamba.
• Figure 4: (Computational Efficiency Eval) FLOPs comparison between STG-Mamba and STAEformer on PeMS04/KnowAir dataset under different STG node number settings.
• Figure 5: Illustration of the spatial-temporal state space selection mechanism that facilitates input-dependent feature selection and focusing.