# MultiSPANS: A Multi-range Spatial-Temporal Transformer Network for Traffic Forecast via Structural Entropy Optimization

arXiv: https://arxiv.org/abs/2311.02880 · HTML: https://mlsanity.com/paper/2311.02880/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 62 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [STAN: Spatio-Temporal Attention Network for Next Location Recommendation](https://mlsanity.com/paper/2102.04095/) (2021)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Coupled Layer-wise Graph Convolution for Transportation Demand Prediction](https://mlsanity.com/paper/2012.08080/) (2020)
- [MTS-Mixers: Multivariate Time Series Forecasting via Factorized Temporal and Channel Mixing](https://mlsanity.com/paper/2302.04501/) (2023)
- [SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization](https://mlsanity.com/paper/2303.09778/) (2023)
- [Hierarchical State Abstraction Based on Structural Information Principles](https://mlsanity.com/paper/2304.12000/) (2023)
- [Effective and Stable Role-Based Multi-Agent Collaboration by Structural Information Principles](https://mlsanity.com/paper/2304.00755/) (2023)
- [Unsupervised Skin Lesion Segmentation via Structural Entropy Minimization on Multi-Scale Superpixel Graphs](https://mlsanity.com/paper/2309.01899/) (2023)

## Built on by (most cited first, 13 of 13)

- [STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Model](https://mlsanity.com/paper/2403.12418/) (2024)
- [Bridging Traffic State and Trajectory for Dynamic Road Network and Trajectory Representation Learning](https://mlsanity.com/paper/2502.06870/) (2025)
- [Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis](https://mlsanity.com/paper/2408.13082/) (2024)
- [Deep Learning for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2503.10198/) (2025)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [XXLTraffic: Expanding and Extremely Long Traffic forecasting beyond test adaptation](https://mlsanity.com/paper/2406.12693/) (2024)
- [ELSPR: Evaluator LLM Training Data Self-Purification on Non-Transitive Preferences via Tournament Graph Reconstruction](https://mlsanity.com/paper/2505.17691/) (2025)
- [Unsupervised Graph Clustering with Deep Structural Entropy](https://mlsanity.com/paper/2505.14040/) (2025)
- [Embracing Large Language Models in Traffic Flow Forecasting](https://mlsanity.com/paper/2412.12201/) (2024)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [Semi-Supervised Clustering via Structural Entropy with Different Constraints](https://mlsanity.com/paper/2312.10917/) (2023)
- [Targeted Adversarial Traffic Generation : Black-box Approach to Evade Intrusion Detection Systems in IoT Networks](https://mlsanity.com/paper/2603.23438/) (2026)
- [F2STNet: Fair and Federated Spectral-Temporal Modeling for Graph Forecasting](https://mlsanity.com/paper/2608.09082/) (2026)

## Abstract (arXiv)

Traffic forecasting is a complex multivariate time-series regression task of paramount importance for traffic management and planning. However, existing approaches often struggle to model complex multi-range dependencies using local spatiotemporal features and road network hierarchical knowledge. To address this, we propose MultiSPANS. First, considering that an individual recording point cannot reflect critical spatiotemporal local patterns, we design multi-filter convolution modules for generating informative ST-token embeddings to facilitate attention computation. Then, based on ST-token and spatial-temporal position encoding, we employ the Transformers to capture long-range temporal and spatial dependencies. Furthermore, we introduce structural entropy theory to optimize the spatial attention mechanism. Specifically, The structural entropy minimization algorithm is used to generate optimal road network hierarchies, i.e., encoding trees. Based on this, we propose a relative structural entropy-based position encoding and a multi-head attention masking scheme based on multi-layer encoding trees. Extensive experiments demonstrate the superiority of the presented framework over several state-of-the-art methods in real-world traffic datasets, and the longer historical windows are effectively utilized. The code is available at https://github.com/SELGroup/MultiSPANS.