# Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting

arXiv: https://arxiv.org/abs/2603.04418 · HTML: https://mlsanity.com/paper/2603.04418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [ST-MLP: A Cascaded Spatio-Temporal Linear Framework with Channel-Independence Strategy for Traffic Forecasting](https://mlsanity.com/paper/2308.07496/) (2023)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2502.12213/) (2025)
- [Stationary time-vertex signal processing](https://mlsanity.com/paper/1611.00255/) (2016)

## Abstract (arXiv)

Standard direct forecasting models typically rely on point-wise objectives such as Mean Squared Error, which fail to capture the complex spatio-temporal dependencies inherent in graph-structured signals. While recent frequency-domain approaches such as FreDF mitigate temporal autocorrelation, they often overlook spatial and cross spatio-temporal interactions. To address this limitation, we propose FreST Loss, a frequency-enhanced spatio-temporal training objective that extends supervision to the joint spatio-temporal spectrum. By leveraging the Joint Fourier Transform (JFT), FreST Loss aligns model predictions with ground truth in a unified spectral domain, effectively decorrelating complex dependencies across both space and time. Theoretical analysis shows that this formulation reduces estimation bias associated with time-domain training objectives. Extensive experiments on six real-world datasets demonstrate that FreST Loss is model-agnostic and consistently improves state-of-the-art baselines by better capturing holistic spatio-temporal dynamics.