# Select, then Balance: Exploring Exogenous Variable Modeling of Spatio-Temporal Forecasting

arXiv: https://arxiv.org/abs/2509.05779 · HTML: https://mlsanity.com/paper/2509.05779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 6 Sep 2025.

## Builds on (most cited first, 30 of 35)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [TEST: Text Prototype Aligned Embedding to Activate LLM's Ability for Time Series](https://mlsanity.com/paper/2308.08241/) (2023)
- [Are Language Models Actually Useful for Time Series Forecasting?](https://mlsanity.com/paper/2406.16964/) (2024)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters](https://mlsanity.com/paper/2308.08469/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [Spatial-Temporal Large Language Model for Traffic Prediction](https://mlsanity.com/paper/2401.10134/) (2024)
- [UrbanGPT: Spatio-Temporal Large Language Models](https://mlsanity.com/paper/2403.00813/) (2024)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [Position: What Can Large Language Models Tell Us about Time Series Analysis](https://mlsanity.com/paper/2402.02713/) (2024)
- [ChronosX: Adapting Pretrained Time Series Models with Exogenous Variables](https://mlsanity.com/paper/2503.12107/) (2025)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)
- [Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2502.12213/) (2025)
- [STBench: Assessing the Ability of Large Language Models in Spatio-Temporal Analysis](https://mlsanity.com/paper/2406.19065/) (2024)
- [ClimateIQA: A New Dataset and Benchmark to Advance Vision-Language Models in Meteorology Anomalies Analysis](https://mlsanity.com/paper/2406.09838/) (2024)
- [Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting](https://mlsanity.com/paper/2410.12593/) (2024)

## Abstract (arXiv)

Spatio-temporal (ST) forecasting is critical for dynamic systems, yet existing methods predominantly rely on modeling a limited set of observed target variables. In this paper, we present the first systematic exploration of exogenous variable modeling for ST forecasting, a topic long overlooked in this field. We identify two core challenges in integrating exogenous variables: the inconsistent effects of distinct variables on the target system and the imbalance effects between historical and future data. To address these, we propose ExoST, a simple yet effective exogenous variable modeling general framework highly compatible with existing ST backbones that follows a "select, then balance" paradigm. Specifically, we design a latent space gated expert module to dynamically select and recompose salient signals from fused exogenous information. Furthermore, a siamese dual-branch backbone architecture captures dynamic patterns from the recomposed past and future representations, integrating them via a context-aware weighting mechanism to ensure dynamic balance. Extensive experiments on real-world datasets demonstrate the ExoST's effectiveness, universality, robustness, and efficiency.