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A General ReLearner: Empowering Spatiotemporal Prediction by Re-learning Input-label Residual

Jiaming Ma, Binwu Wang, Pengkun Wang, Xu Wang, Zhengyang Zhou, Yang Wang

TL;DR

This work tackles the limitation of forward spatiotemporal prediction models by addressing spatiotemporal input–label deviation. It introduces Spatiotemporal Residual Theory based on Gaussian Markov Random Fields and a universal module, ReLearner, that adds a backward residual correction pathway to existing STNNs. The method disentangles and propagates residuals between input and label representations via a residual learning and smoothing pipeline, yielding improved accuracy across 11 real-world datasets and 14 backbone models, with gains up to about 21%. ReLearner remains computationally efficient, compatible with diverse architectures, and demonstrates robust performance under both spatial and temporal deviations, making it a practical enhancement for real-world spatiotemporal forecasting tasks.

Abstract

Prevailing spatiotemporal prediction models typically operate under a forward (unidirectional) learning paradigm, in which models extract spatiotemporal features from historical observation input and map them to target spatiotemporal space for future forecasting (label). However, these models frequently exhibit suboptimal performance when spatiotemporal discrepancies exist between inputs and labels, for instance, when nodes with similar time-series inputs manifest distinct future labels, or vice versa. To address this limitation, we propose explicitly incorporating label features during the training phase. Specifically, we introduce the Spatiotemporal Residual Theorem, which generalizes the conventional unidirectional spatiotemporal prediction paradigm into a bidirectional learning framework. Building upon this theoretical foundation, we design an universal module, termed ReLearner, which seamlessly augments Spatiotemporal Neural Networks (STNNs) with a bidirectional learning capability via an auxiliary inverse learning process. In this process, the model relearns the spatiotemporal feature residuals between input data and future data. The proposed ReLearner comprises two critical components: (1) a Residual Learning Module, designed to effectively disentangle spatiotemporal feature discrepancies between input and label representations; and (2) a Residual Smoothing Module, employed to smooth residual terms and facilitate stable convergence. Extensive experiments conducted on 11 real-world datasets across 14 backbone models demonstrate that ReLearner significantly enhances the predictive performance of existing STNNs.Our code is available on GitHub.

A General ReLearner: Empowering Spatiotemporal Prediction by Re-learning Input-label Residual

TL;DR

This work tackles the limitation of forward spatiotemporal prediction models by addressing spatiotemporal input–label deviation. It introduces Spatiotemporal Residual Theory based on Gaussian Markov Random Fields and a universal module, ReLearner, that adds a backward residual correction pathway to existing STNNs. The method disentangles and propagates residuals between input and label representations via a residual learning and smoothing pipeline, yielding improved accuracy across 11 real-world datasets and 14 backbone models, with gains up to about 21%. ReLearner remains computationally efficient, compatible with diverse architectures, and demonstrates robust performance under both spatial and temporal deviations, making it a practical enhancement for real-world spatiotemporal forecasting tasks.

Abstract

Prevailing spatiotemporal prediction models typically operate under a forward (unidirectional) learning paradigm, in which models extract spatiotemporal features from historical observation input and map them to target spatiotemporal space for future forecasting (label). However, these models frequently exhibit suboptimal performance when spatiotemporal discrepancies exist between inputs and labels, for instance, when nodes with similar time-series inputs manifest distinct future labels, or vice versa. To address this limitation, we propose explicitly incorporating label features during the training phase. Specifically, we introduce the Spatiotemporal Residual Theorem, which generalizes the conventional unidirectional spatiotemporal prediction paradigm into a bidirectional learning framework. Building upon this theoretical foundation, we design an universal module, termed ReLearner, which seamlessly augments Spatiotemporal Neural Networks (STNNs) with a bidirectional learning capability via an auxiliary inverse learning process. In this process, the model relearns the spatiotemporal feature residuals between input data and future data. The proposed ReLearner comprises two critical components: (1) a Residual Learning Module, designed to effectively disentangle spatiotemporal feature discrepancies between input and label representations; and (2) a Residual Smoothing Module, employed to smooth residual terms and facilitate stable convergence. Extensive experiments conducted on 11 real-world datasets across 14 backbone models demonstrate that ReLearner significantly enhances the predictive performance of existing STNNs.Our code is available on GitHub.
Paper Structure (22 sections, 33 equations, 7 figures, 12 tables, 1 algorithm)

This paper contains 22 sections, 33 equations, 7 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Spatiotemporal Prediction
  4. Out-of-Distribution in Spatiotemporal Learning
  5. Preliminaries
  6. Method
  7. Spatiotemporal Residual Theory based on Gaussian Markov Random Field
  8. ReLearner based on Spatiotemporal Residual Theory
  9. Forward Spatiotemporal Learning
  10. Backward Residual Correction
  11. Residual Propagation Kernel
  12. Experiment
  13. Experimental Setup
  14. Analysis of Predictive Performance (RQ1)
  15. Effectiveness in Handling Spatiotemporal Input–Label Deviation (RQ2)
  16. ...and 7 more sections

Figures (7)

  • Figure 1: Visualization examples of input-label deviation on LargeST-SD dataset: (a, left) similar histories produce divergent lables; (b, middle) different inputs yield similar lables; and (c, right) abrupt, atypical temporal shifts.
  • Figure 2: The overall framework of ReLearner for spatiotemporal learning. ReLearner extends the forward learning process of STNNs by supplementing it with a backward learning process to explicitly model residual information.
  • Figure 3: Visualization of prediction comparison between PM$_{2.5}$GNN and it with ReLearner on KnowAir (Left) and LargeST-GLA (Right).
  • Figure 4: Visualization cases of input-label deviation.
  • Figure 5: A comparison of the convergence speed and convergence results in validation phase of baselines without ReLearner and with ReLearner on the LargeST-SD dataset.
  • ...and 2 more figures