PaperlayerView exact revision on arXiv

Source-linked AI summary

AdaST: Adaptive Coupling for Spatial-Temporal Forecasting

Zhenyu Lei, Chenghao Liu, Yushun Dong, Qi R. Wang, Jundong Li

arXiv:2609.36119v1cs.AI

TL;DR

Existing spatial-temporal forecasting methods often assume strong coupling, although real-world data includes temporal-dominated, spatial-dominated, and strongly coupled regimes. AdaST decomposes inputs into coupling-specific components and adaptively recombines them; across four benchmarks, it achieves state-of-the-art results with reported average improvements over the strongest competitors.

  • Problem

    Real-world spatial-temporal data has distinct coupling regimes, but existing methods commonly apply uniform strongly coupled architectures that can exploit spurious associations and perform suboptimally.

    Source: §1 · p. 2, §2.2 · p. 3

  • Method

    AdaST uses heterogeneity-aware experts to decompose inputs into temporal, spatial, and joint components, processes them with aligned modules, and adaptively recombines them with correlation-informed modulation.

    Source: §1 · p. 2, §3 · p. 4, §3.3 · p. 6

  • Results

    Across four benchmarks, AdaST achieves state-of-the-art results, improving MAE by up to 1.7%, RMSE by 0.7%, and MAPE by 0.8% on average over the strongest baselines.

    Source: §4.2 · p. 7

  • Takeaways & Limitations

    The results support aligning spatial and temporal modeling with intrinsic coupling structures rather than applying uniform architectural priors.

    Source: §6 · p. 10

    The evaluation focuses on short-term forecasting with fixed input and output lengths of 12 time steps; long-term forecasting remains open, and the paradigm may increase memory use on very large graphs.

    Source: §F.1 · p. 21

Abstract

from arXiv · show

Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

1 Introduction

Spatial-temporal data spans temporal-dominated, spatial-dominated, and strongly coupled regimes, while many existing methods assume strong, homogeneous coupling. AdaST adapts its spatial and temporal modeling to these structures and outperforms baselines across diverse benchmarks.

1 Introduction

  • Real-world data spans temporal-dominated, spatial-dominated, and strongly coupled regimes, so uniformly applying coupled models can introduce spurious dependencies and degrade forecasting.Coupling strength can also vary across regions and time periods within a dataset.Source: §1 · p. 2
  • The framework addresses unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling, including noisy learned graphs and costly or spurious all-pairs attention.Its experts use learned embeddings to guide decomposition according to location- and period-specific characteristics.Source: §1 · p. 2
  • AdaST decomposes inputs into temporal-specific, spatial-specific, and jointly coupled components, processes each with a role-aligned module, then adaptively recombines them for prediction.Correlation-informed modulation further reduces spurious correlations within components.Source: §1 · p. 2
  • AdaST consistently outperforms all baselines across diverse benchmarks.Its heterogeneity-aware experts capture spatial and temporal variation through learned embeddings that guide decomposition.Source: §1 · p. 2

2 Preliminaries

The preliminaries formulate forecasting from historical observations across locations, distinguish three spatial-temporal coupling regimes, and use synthetic experiments to examine whether architecture matches regime. Those experiments report better normalized MAE for aligned architectures across tested backbones.

2.1 Spatial-Temporal Forecasting

  • Spatial-temporal forecasting maps historical observations across locations to predictions over the next T′ time steps, optionally using an adjacency matrix for known connectivity.The input is represented as a tensor over nodes, historical time steps, and features.Source: §2.1 · p. 3

2.2 Coupling Structure

  • The preliminaries distinguish temporal-dominated, spatial-dominated, and strongly coupled data; applying one strongly coupled architecture across regimes can encourage spurious associations and suboptimal performance.Temporal-dominated cases emphasize each location’s history, spatial-dominated cases emphasize recent propagation from other nodes, and strongly coupled cases require both.Source: §2.2 · p. 3

2.3 Preliminary Experiments

  • The preliminary experiments construct synthetic datasets for the three regimes and report that their measured correlation coefficients match the intended structures.The experiments compare temporal-only, spatial-only, and joint spatial-temporal architectures across four backbone variants.Source: §2.3 · pp. 3–4, Table 1 · p. 3
  • Across all tested backbones, Figure 1 shows the darkest normalized-MAE results for architecture–data matches, while mismatches show significant performance degradation.The reported pattern suggests more expressive backbones have larger performance gaps when architectures mismatch the underlying coupling structure.Source: §2.3 · p. 4, Figure 1 · p. 4

3 Methodology

AdaST decomposes spatial-temporal inputs into components with distinct coupling patterns, processes them through role-aligned modules, and adaptively recombines them using learned gates and correlation information.

3 Methodology

  • AdaST’s framework has three modules: heterogeneity-aware decoupling, spatial-temporal modeling, and correlation-regularized recoupling.Figure 2 uses different colors to denote different components.Source: §3 · p. 4, Figure 2 · p. 5

3.1 Heterogeneity-Aware Decomposition

  • Four experts provide spatial, time-of-day, day-of-week, and joint spatiotemporal perspectives for decomposing inputs into distinct coupling patterns.Their learned contextual embeddings represent location- and time-specific attributes.Source: §3.1 · p. 5

3.2 Spatial-Temporal Modeling

  • Temporal-specific components use attention, spatial-specific components use spatial mixers, and coupled components interleave temporal and spatial operations.The spatial mixer captures pairwise spatial interactions without a predefined graph or substantial computation overhead.Source: §3.2 · pp. 5–6

3.3 Correlation-Informed Recomposition

  • A gated network assigns component weights from their representations, then temporal projection and an output layer generate predictions.The model adjusts component contributions based on input characteristics and learned patterns.Source: §3.3 · p. 6
  • Cosine-similarity correlation measures for temporal and spatial components, and their average for the coupled component, modulate gate scores before softmax weighting.The correlation influence is controlled by α.Source: §3.3 · p. 6
  • AdaST achieves the best performance across all datasets in the PurpleAir and PEMS benchmarks.The table caption identifies these as the main results.Source: Table 2 · p. 7

4 Experiments

Experiments evaluate AdaST on four benchmarks and compare it with 16 baselines. Results cover benchmark performance, module ablations, dataset coupling patterns, changing gate scores, and learned component representations.

4.1 Experimental Settings

  • Evaluations use PEMS04, PEMS07, PEMS08, and PurpleAir, comparing 16 baselines and reporting MAE, RMSE, and MAPE averaged across 12 prediction horizons.All datasets use 60/20/20 train/validation/test splits; inputs and prediction horizons are 12 time steps.Source: §4.1 · p. 7

4.2 Main Results

  • AdaST achieves state-of-the-art results across four benchmarks, improving MAE by up to 1.7%, RMSE by 0.7%, and MAPE by 0.8% over the strongest competitors on average.The largest reported gain is 4.3% in MAE on PurpleAir.Source: §4.2 · pp. 7–8

4.3 Ablation Study

  • Ablations show all four experts contribute, with the spatial expert most important on PurpleAir and the time-of-day expert most important on PEMS07.Spatial attention degrades performance, especially on temporal-dominated PurpleAir; removing learned gates or correlation measures also harms recomposition.Source: §4.3 · p. 8, Table 3 · p. 8

4.4 Coupling Structure Analysis

  • Average gate scores reveal distinct dataset coupling: traffic benchmarks are relatively spatial-dominant, while PurpleAir and BeijingAirQuality have higher temporal gate scores.ETTh and ETTm show substantial cross-feature coupling, with spatial gate scores comparable to temporal ones.Source: §4.4 · pp. 8–9, Figure 3 · p. 8

4.5 Case Study

  • On PEMS07, gate scores are relatively stable across the dataset yet show periodic variation across time and distinct coupling patterns by location.Temporal gates peak during gradual changes, spatial gates spike during abrupt shifts, and the spatiotemporal gate rises when temporal and spatial scores are comparable.Source: §4.5 · p. 9

4.6 Representation Analysis

  • A t-SNE visualization shows clear separation among temporal, spatial, and spatiotemporal component representations before recomposition.The authors interpret the separated clusters as evidence of component specialization.Source: §4.6 · p. 9, Figure 4 · p. 9

5 Related Works

Prior work ranges from temporal-only forecasting to models that jointly capture spatial and temporal dependencies. The section identifies fixed decomposition and recomposition as gaps that AdaST addresses with adaptive coupling.

Prior forecasting approaches

  • Temporal-only methods model each series independently, while coupled models use graph or attention architectures to capture spatial dependencies alongside temporal patterns.Examples include DCRNN, STGCN, and GWNet for graph-based modeling and GMAN and STAEformer for attention-based modeling.Source: §5 · p. 9

Decoupling and decomposition

  • The section argues that varying coupling structures can make uniform architectural assumptions produce spurious correlations, while D2STGNN decomposes only temporal and spatiotemporal components and uses fixed recomposition.AdaST is presented as adaptively coupling spatial and temporal signals.Source: §5 · p. 9

Representation visualization

  • A t-SNE visualization shows separated learned representations for temporal, spatial, and spatial-temporal-coupling components.The visualization is described as demonstrating disentanglement.Source: Figure 5 · p. 9

6 Conclusion

The conclusion frames variable coupling structures as a mismatch for uniform architectural priors and presents AdaST as an adaptive decompose-recompose framework. It reports consistent benchmark gains and interpretable dataset-specific coupling insights.

6 Conclusion

  • Coupling structures vary across datasets, while existing approaches apply uniform architectural priors that do not accommodate this variability.The conclusion identifies this mismatch as a central challenge in spatial-temporal forecasting.Source: §6 · p. 10
  • AdaST disentangles temporal-specific, spatial-specific, and spatiotemporally coupled patterns, then recombines them adaptively according to the data.The framework is described as aligning model inductive biases with intrinsic coupling structures.Source: §6 · p. 10
  • The conclusion reports consistent outperformance of state-of-the-art baselines across diverse benchmarks and interpretable insights into dataset-specific coupling.Source: §6 · p. 10

Appendix Overview

  • Appendix figures depict temporal-dominated, spatial-dominated, and strongly coupled synthetic datasets, and contrast temporal autocorrelation in TD and SD data.Source: Figure 6 · p. 15, Figure 7 · p. 15

A Synthetic Dataset Details

The appendix describes synthetic spatial-temporal datasets with distinct temporal, spatial, and combined coupling patterns. Qualitative examples and correlation measurements are used to characterize those regimes.

Data Generation

  • Each synthetic dataset contains 10 spatially distributed time series of 200 time steps; the spatial-dominated dataset uses a directed sparse graph with edge density 0.43.Source: A Synthetic Dataset Details · p. 15

Qualitative Analysis

  • TD trajectories are smooth and rely on historical information, SD trajectories are volatile and rely on recent neighbor information, and SC combines smooth trends with spatial propagation.Source: A Synthetic Dataset Details · p. 15

Quantitative Correlation Analysis

  • TD has temporal correlation 0.63±0.07 and spatial correlation −0.05 ± 0.06; SD has spatial correlation 0.33 ± 0.12 and temporal correlation 0.25 ± 0.01; SC has temporal correlation 0.54±0.05 and spatial correlation 0.21 ± 0.02.The authors describe these measurements as validating the construction of three distinct coupling regimes.Source: A Synthetic Dataset Details · p. 15

B Implementation and Efficiency Analysis

AdaST uses a fixed configuration for its efficiency analysis and its spatial mixer trains faster per epoch than spatial attention across the four main benchmarks.

B Implementation and Efficiency Analysis

C Additional Main Results

On additional financial, energy, and traffic benchmarks, AdaST achieves the best average rank, while the relative performance of spatial-temporal and time-series-only baselines varies with spatial correlation.

C Additional Main Results

  • MAE is the primary reported metric because missing data and zero values make RMSE and MAPE unstable on some datasets.The additional comparison includes PatchTST and DLinear, alongside graph-free spatial-temporal baselines STID, HimNet, and STNorm.Source: C Additional Main Results · p. 17
  • AdaST achieves the best average rank across ExchangeRate, ETTh1, and METR-LA, extending its reported generalizability beyond the main paper’s traffic and air-quality domains.The comparison also includes PEMS08; the results are presented in Table 5.Source: C Additional Main Results · p. 17, Table 5 · p. 17
  • Spatial-temporal baselines generally match or outperform time-series-only methods on datasets with non-negligible spatial correlations, including METR-LA and PEMS08.The passage contrasts this pattern with temporally dominated datasets, where time-series-only methods outperform spatial-temporal counterparts.Source: C Additional Main Results · p. 17

D Additional Ablation Study

Additional PEMS ablations identify contributions from heterogeneity-aware experts, learned gates, and correlation measures; correlation measures also correspond with gate scores across datasets.

D Additional Ablation Study

  • Removing the time-of-day expert causes the largest performance degradation on PEMS04 and PEMS08, although all four heterogeneity-aware experts contribute.The relative importance of the experts varies across datasets; Table 6 reports the ablations.Source: D Additional Ablation Study · p. 18, Table 6 · p. 18
  • Replacing the spatial mixer with spatial attention yields only marginal differences on PEMS04 and PEMS08.The passage contrasts this with temporal-dominated PurpleAir, where attention introduces spurious long-range correlations.Source: D Additional Ablation Study · p. 18, Table 6 · p. 18
  • Both learned gate scores and correlation measures are essential for effective recomposition across diverse coupling structures.Figure 9 presents normalized correlation measures across datasets and reports strong correspondence with gate scores in Figure 3.Source: D Additional Ablation Study · p. 18, Figure 9 · p. 19

E.1 Correlation Measure Analysis

Correlation measures track gate scores and show relationships among temporal, spatial, and spatiotemporal components; case studies show temporal and spatial variation in learned gates.

E.1 Correlation Measure Analysis

  • Datasets with high spatial correlation measures, such as PEMS, also have high spatial gate scores, and the measures correspond with gate scores across datasets.The analysis treats both as reflecting each component’s information content and reliability.Source: §E.1 · p. 19
  • Temporal and spatial correlation measures are negatively related, while temporal and spatiotemporal measures are positively related.The passage attributes the latter relationship to reduced spatial correlation enhancing temporal and spatiotemporal correlations, with the spatiotemporal component capturing residual joint patterns.Source: §E.1 · p. 19

E.2 Additional Case Studies

  • In PEMS07, more accurate predictions correlate with more dynamic gate scores; Figure 11 shows this for locations 0 and 1.Location 0 has better accuracy and more turbulent gate-score trajectories than location 1.Source: §E.2 · p. 19, Figure 11 · p. 20
  • Across 160 locations, gate scores are broadly similar but vary at some locations, supporting the use of spatial heterogeneity experts.Figure 12 visualizes the gate-score distributions for a fixed time period.Source: §E.2 · pp. 19–20, Figure 12 · p. 21

F.1 Limitation

The paper identifies memory costs at very large node counts and short-term evaluation with fixed 12-step input and output lengths as limitations. It also discusses potential benefits and deployment risks, while reporting its claims, reproducibility details, and experimental significance practices.

F.1 Limitation

  • AdaST adds parameters that may increase memory use on datasets with very many nodes, and its evaluation covers only short-term forecasting with fixed 12-step inputs and outputs.Long-term forecasting is left as future work.Source: §F.1 · p. 21

F.2 Broader Impact

  • The paper identifies improved forecasting reliability as a potential benefit and flags overconfident decisions, distribution shift, and sensor-data bias as risks.It recommends domain-specific validation, drift monitoring, and transparency about uncertainty.Source: §F.2 · p. 21, §7 · p. 23

1. Claims

  • The abstract and introduction are reported to reflect AdaST’s coupling-mismatch motivation, decompose-recompose framework, and benchmark performance claims; the paper has no formal theoretical results or proofs.Its coupling formulations are descriptive definitions used to motivate the framework.Source: §1 · p. 22
  • The paper reports 60/20/20 data splits, Z-score normalization, optimizer and hyperparameter settings, and an anonymized code repository for reproducing results.Appendix B describes hyperparameter selection by grid search.Source: §1 · p. 22, §7 · p. 24

7. Experiment statistical significance

  • Error bars are not reported because repeated runs across 16 baselines on four datasets were computationally costly; results use the single-run protocol used for the baselines.Source: §7 · p. 23

1. Claims

  • Baselines use their official implementations with recommended hyperparameters, and the datasets and baseline methods are credited.Source: §7 · p. 23
Loading 2609.36119v1…