# ST-Hyper: Learning High-Order Dependencies Across Multiple Spatial-Temporal Scales for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2509.02217 · HTML: https://mlsanity.com/paper/2509.02217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Memory Networks](https://mlsanity.com/paper/1410.3916/) (2014)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [MSGNet: Learning Multi-Scale Inter-Series Correlations for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2401.00423/) (2023)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [Group-Aware Graph Neural Network for Nationwide City Air Quality Forecasting](https://mlsanity.com/paper/2108.12238/) (2021)
- [Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecasting](https://mlsanity.com/paper/2410.23992/) (2024)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [FilterTS: Comprehensive Frequency Filtering for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.04158/) (2025)
- [WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correction](https://mlsanity.com/paper/2310.05517/) (2023)

## Built on by (most cited first, 2 of 2)

- [Multi-scale hypergraph meets LLMs: Aligning large language models for time series analysis](https://mlsanity.com/paper/2602.04369/) (2026)
- [Coordinated Disentanglement with Iterative Mode Discovery Under Hidden Correlations](https://mlsanity.com/paper/2607.17264/) (2026)

## Abstract (arXiv)

In multivariate time series (MTS) forecasting, many deep learning based methods have been proposed for modeling dependencies at multiple spatial (inter-variate) or temporal (intra-variate) scales. However, existing methods may fail to model dependencies across multiple spatial-temporal scales (ST-scales, i.e., scales that jointly consider spatial and temporal scopes). In this work, we propose ST-Hyper to model the high-order dependencies across multiple ST-scales through adaptive hypergraph modeling. Specifically, we introduce a Spatial-Temporal Pyramid Modeling (STPM) module to extract features at multiple ST-scales. Furthermore, we introduce an Adaptive Hypergraph Modeling (AHM) module that learns a sparse hypergraph to capture robust high-order dependencies among features. In addition, we interact with these features through tri-phase hypergraph propagation, which can comprehensively capture multi-scale spatial-temporal dynamics. Experimental results on six real-world MTS datasets demonstrate that ST-Hyper achieves the state-of-the-art performance, outperforming the best baselines with an average MAE reduction of 3.8% and 6.8% for long-term and short-term forecasting, respectively.