DST-Net: Decomposed Spatio-Temporal Network for Time Series Forecasting

• Existing decomposition methods often apply identical architectures to trend and seasonal components, overlooking their distinct properties.The paper argues that this uniform modeling limits representation capability.Source: §1 · p. 2
• Trend components show synchronized behavior and strong cross-variable correlation, so trend modeling requires spatial dependencies beyond temporal information alone.Daily traffic peaks are described as a shared system state that can synchronize congestion across sensors.Source: §1 · pp. 2–3
• Seasonal components exhibit local continuity, periodicity, and positive autocorrelation peaks at Lag 24, supporting a focus on temporal self-evolution.The passage contrasts this temporal dependence with external spatial factors.Source: §1 · p. 3
• DST-Net uses a Latent Graph Block for trend dependencies and Gaussian Multi-scale Attention with learnable priors for multi-granular seasonal contexts.The seasonal mechanism is designed to filter global noise while capturing local evolution and phase shifts.Source: §1 · p. 3

2.1 Deep Time Series Forecasting Paradigms

• Early Transformer forecasters such as Informer and Autoformer used channel mixing to capture latent correlations, but this strategy can entangle noise and signals.The passage notes that this can lead to overfitting and inferior performance to simple linear baselines such as DLinear.Source: §2.1 · pp. 3–4
• Channel-independent methods such as PatchTST [15] and TiDE [4] improve robustness and data efficiency but sacrifice cross-variable dependency modeling.Source: §2.1 · p. 4
• Hybrid approaches and Mamba-based forecasters [5] model cross-variate interactions, while DST-Net tailors strategies to decomposed components.Examples include MambaTS, which learns variable-aware scan orders, and TimePro, which constructs variable- and time-aware hyper-states.Source: §2.1 · p. 4

3.1 Problem Definition and Overall Architecture

• Forecasting requires predicting future multivariate observations from historical data while disentangling coupled spatiotemporal dependencies in non-stationary sequences.Source: §3.1 · p. 4
• A moving-average decomposition separates each sequence into trend and seasonal components, which DST-Net processes through parallel branches before aggregating their forecasts.Source: §3.1 · pp. 4–5

3.2 Seasonal Branch: Gaussian Multi-scale Attention

• Vanilla global attention can overemphasize distant, numerically similar points from different seasonal phases, whereas local context helps preserve waveform continuity and phase transitions.Source: Motivation · pp. 5–6
• GMA adds learnable, distance-based Gaussian priors to attention scores, with head bandwidths spanning narrow, medium, wide, and unconstrained global views.Source: Gaussian Multi-scale Attention · pp. 6–7

3.3 Trend Branch: Latent Graph Block

• The Latent Graph Block represents each variate’s history as a latent node and uses sparse cross-variate attention to capture trend dependencies.Source: §3.3 · p. 7
• A shared prediction head maps the updated latent nodes to future trend values for each variate.Source: §3.3 · p. 7

4.1 Experimental Setup

• Long-term experiments cover seven benchmarks at four prediction horizons, while short-term experiments use PEMS04 with a 96-step input and 12-step horizon.Source: §4.1 · p. 8
• Comparisons include multi-scale, variate-wise, and patch-based models under identical data splits and preprocessing.Source: §4.1 · p. 8

4.2 Evaluation Metrics

• Long-term forecasting is evaluated with MSE and MAE, while short-term forecasting uses MAE, RMSE, and MAPE; lower values are better.Source: §4.2 · p. 8

4.3 Long-term Forecasting

• DST-Net achieves leading average performance on most benchmarks and consistently ranks among the strongest methods across prediction horizons.Its competitive MSE and MAE at shorter and longer horizons indicate gains across the evaluated forecasting ranges.Source: §4.3 · p. 8, Table 1 · p. 9
• DST-Net leads in both average metrics on Exchange and Traffic, remains competitive on ETT series and Weather, and trails TimeMixer on ETTm2.The ETTm2 result illustrates that relative benefits vary across datasets.Source: §4.3 · p. 8
• The results suggest that adapting modeling to each decomposed component is beneficial for long-term forecasting.The Latent Graph Block targets cross-variate trend dependencies, while Gaussian Multi-scale Attention models seasonal evolution at multiple temporal scales.Source: §4.3 · p. 8

4.4 Short-term Forecasting

• DST-Net reduces MAPE, RMSE, and MAE versus reproduced TimeMixer by 12.5%, 2.5%, and 1.0%, respectively.The comparison uses PEMS04 with 96 historical observations to predict 12 time steps; TimeMixer is reproduced under the same setting.Source: §4.4 · p. 9, Table 2 · p. 10
• In PEMS04, shared road conditions influence traffic states across sensors, and the Latent Graph Block aggregates relevant sensors to model correlated trend variations.Gaussian Multi-scale Attention models local fluctuations and recurring temporal patterns at different granularities.Source: §4.4 · pp. 9–10
• The two branches capture cross-sensor co-movements and short-term temporal dynamics, consistent with DST-Net’s reported effectiveness on both long- and short-term forecasting.The Latent Graph Block targets correlated trend variations, while Gaussian Multi-scale Attention models local and recurring patterns.Source: §4.4 · p. 10

4.5 Effectiveness of Different Components

• Removing decomposition consistently increases average MSE; removing the Latent Graph Block raises Exchange MSE from 0.339 to 0.368, while removing Gaussian Multi-scale Attention raises Weather MSE from 0.239 to 0.263.The variants respectively bypass decomposition, remove the Latent Graph Block, or replace Gaussian Multi-scale Attention with vanilla self-attention.Source: §4.5 · p. 10, Table 4 · p. 11

4.6 Effectiveness of Component-specific Modeling

• Both homogeneous variants underperform the complete model, indicating that a single strategy overlooks differences between decomposed components.The alternatives apply Gaussian Multi-scale Attention or the Latent Graph Block to both components.Source: §4.6 · pp. 10–11
• Swapping the branch strategies increases average MSE from 0.339/0.418/0.239 to 0.367/0.443/0.267 on Exchange, ETTh1, and Weather, respectively.The authors report the largest degradation for the Swapped design, supporting the assignment of Gaussian Multi-scale Attention to seasonal evolution and the Latent Graph Block to cross-variate trends.Source: §4.6 · p. 11

4.7 Effectiveness of Different Gaussian Scales in GMA

• The full Narrow, Medium, Wide, and Global configuration achieves a superior MSE of 0.239 on Weather.Single-scale Narrow or Medium variants capture specific temporal granularities but yield suboptimal results; the multi-scale priors filter high-frequency noise while retaining long-term periodic dependencies.Source: §4.7 · p. 11

4.8 Qualitative Analysis: Component Disentanglement

• Figure 4 compares the ground-truth decomposition with trend-branch, seasonal-branch, and full-sequence predictions.Source: Figure 4 · p. 12
• The reconstructed sequence follows the overall temporal pattern, with trend and seasonal branches providing complementary forecasting information.The trend prediction follows smooth evolution, while the seasonal prediction captures recurring oscillations.Source: §4.8 · pp. 11–12
• The seasonal branch underestimates an isolated abrupt peak, indicating that rare high-amplitude events remain challenging.Source: §4.8 · p. 12

5 Conclusion

• DST-Net consistently outperforms leading models in both long-term and short-term forecasting tasks.Source: §5 · p. 12
• The architecture uses a Latent Graph Block for trend co-movements and Gaussian Multi-scale Attention to mitigate seasonal attention distraction.Source: §5 · p. 12
• DST-Net addresses inductive-bias conflicts by modeling globally spatially coupled trends and locally evolving seasonal components differently.Source: §5 · p. 12