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

arXiv: https://arxiv.org/abs/2403.12418 · HTML: https://mlsanity.com/paper/2403.12418/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Video, motion and generative Mamba models, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 17 of 17)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Spatial-Temporal Transformer for Dynamic Scene Graph Generation](https://mlsanity.com/paper/2107.12309/) (2021)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting](https://mlsanity.com/paper/2002.12898/) (2020)
- [Knowledge-aware Coupled Graph Neural Network for Social Recommendation](https://mlsanity.com/paper/2110.03987/) (2021)
- [Group-Aware Graph Neural Network for Nationwide City Air Quality Forecasting](https://mlsanity.com/paper/2108.12238/) (2021)
- [DisenHAN: Disentangled Heterogeneous Graph Attention Network for Recommendation](https://mlsanity.com/paper/2106.10879/) (2021)
- [MultiSPANS: A Multi-range Spatial-Temporal Transformer Network for Traffic Forecast via Structural Entropy Optimization](https://mlsanity.com/paper/2311.02880/) (2023)

## Built on by (most cited first, 24 of 24)

- [Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges](https://mlsanity.com/paper/2404.16112/) (2024)
- [State Space Model for New-Generation Network Alternative to Transformers: A Survey](https://mlsanity.com/paper/2404.09516/) (2024)
- [NetMamba: Efficient Network Traffic Classification via Pre-training Unidirectional Mamba](https://mlsanity.com/paper/2405.11449/) (2024)
- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)
- [DyGMamba: Efficiently Modeling Long-Term Temporal Dependency on Continuous-Time Dynamic Graphs with State Space Models](https://mlsanity.com/paper/2408.04713/) (2024)
- [SpoT-Mamba: Learning Long-Range Dependency on Spatio-Temporal Graphs with Selective State Spaces](https://mlsanity.com/paper/2406.11244/) (2024)
- [ST-Mamba: Spatial-Temporal Mamba for Traffic Flow Estimation Recovery using Limited Data](https://mlsanity.com/paper/2407.08558/) (2024)
- [How Different from the Past? Spatio-Temporal Time Series Forecasting with Self-Supervised Deviation Learning](https://mlsanity.com/paper/2510.04908/) (2025)
- [Mamba State-Space Models Are Lyapunov-Stable Learners](https://mlsanity.com/paper/2406.00209/) (2024)
- [Exploring Graph Mamba: A Comprehensive Survey on State-Space Models for Graph Learning](https://mlsanity.com/paper/2412.18322/) (2024)
- [Technologies on Effectiveness and Efficiency: A Survey of State Spaces Models](https://mlsanity.com/paper/2503.11224/) (2025)
- [A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction](https://mlsanity.com/paper/2506.13678/) (2025)
- [Damba-ST: Domain-Adaptive Mamba for Efficient Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2506.18939/) (2025)
- [Venturing into Uncharted Waters: The Navigation Compass from Transformer to Mamba](https://mlsanity.com/paper/2406.16722/) (2024)
- [AI-Driven Forecasting and Monitoring of Urban Water System](https://mlsanity.com/paper/2510.06631/) (2025)
- [NetMamba+: A Framework of Pre-trained Models for Efficient and Accurate Network Traffic Classification](https://mlsanity.com/paper/2601.21792/) (2026)
- [GAMMA-Net: Adaptive Long-Horizon Traffic Spatio-Temporal Forecasting Model based on Interleaved Graph Attention and Multi-Axis Mamba](https://mlsanity.com/paper/2604.16859/) (2026)
- [Focus Where It Matters: Graph Selective State Focused Attention Networks](https://mlsanity.com/paper/2410.15849/) (2024)
- [Coden: Efficient Temporal Graph Neural Networks for Continuous Prediction](https://mlsanity.com/paper/2602.12613/) (2026)
- [Graph Mamba Survival Analysis Based on Topology-Aware ordering](https://mlsanity.com/paper/2606.02602/) (2026)
- [State Space Models Meet Remote Sensing: A Survey](https://mlsanity.com/paper/2606.25329/) (2026)
- [F2STNet: Fair and Federated Spectral-Temporal Modeling for Graph Forecasting](https://mlsanity.com/paper/2608.09082/) (2026)
- [Graph-MambaNav: Spatial-Temporal Graph Mamba Leveraging Object-Relation Knowledge for Object-Goal Navigation](https://mlsanity.com/paper/2608.13723/) (2026)
- [Social Graph Mamba: Forecasting Pedestrian Movements Based on Social Context](https://mlsanity.com/paper/2608.21411/) (2026)

## Abstract (arXiv)

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: urlhttps://github.com/LincanLi98/STG-Mamba.