Research map / Time series / Long-term forecasting
CMoS: Rethinking Time Series Prediction Through the Lens of Chunk-wise Spatial Correlations
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Proposes CMoS, a super-lightweight multivariate forecaster that models chunk-to-chunk spatial correlation matrices, mixes K shared correlation matrices per channel via learned weights, and optionally injects periodicity by initializing one matrix.
Problem
Long-term multivariate time series forecasting with extremely small parameter budgets; lightweight channel-independent models can only represent one temporal structure, and point-wise linear models are sensitive to noise.
Approach
Model forecasting as learned linear mappings between chunks of historical and future windows (chunk-wise spatial correlations), and mix a small set of shared correlation matrices with channel-specific weights produced by convolutional aggregators and a shared linear allocator, plus a periodic initialization of one matrix.
Key results
- CMoS achieves MSE 0.129 on Electricity and 0.367 on Traffic at horizon 96, matching or beating CycleNet and PatchTST among compared models.
- CMoS uses roughly 1% of DLinear's parameter count on ETTh1 per the parameter analysis, and inference FLOPs of 2.96G versus 5.31G for DLinear on Electricity.
- Correlation Mixing ablation improves Weather MSE at horizon 96 from 0.171 to 0.144 (about 17.5%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Correlation Mixing (ablation) | CMoS · Electricity, Traffic, Weather, ETTh1, ETTh2, ETTm1, ETTm2 (horizon 96) | MSE: 0.137 -> 0.129; 0.385 -> 0.367; 0.171 -> 0.144; 0.362 -> 0.361; 0.276 -> 0.274; 0.308 -> 0.292; 0.168 -> 0.167 | Helped |
| use chunk-wise modeling instead of chunk size 1 (ablation) | CMoS · Electricity, Traffic, Weather, ETTh1, ETTh2, ETTm1, ETTm2 (horizon 96) | MSE: 0.132 -> 0.129; 0.368 -> 0.367; 0.147 -> 0.144; 0.368 -> 0.361; 0.280 -> 0.274; 0.288 -> 0.292; 0.170 -> 0.167 | Mixed |
| add Periodicity Injection (ablation) | CMoS · Electricity, Traffic, Weather, ETTh1, ETTh2, ETTm1, ETTm2 (horizon 96) | MSE: 0.130 -> 0.129; 0.369 -> 0.367; 0.144 -> 0.148; 0.366 -> 0.361; 0.292 -> 0.274; 0.293 -> 0.292; 0.170 -> 0.167 | Mixed |
| use CMoS rather than the strongest baseline | long-term multivariate forecasting · Electricity, Traffic, Weather, ETTh1, ETTh2 (all horizons) | MSE | Mixed |
Surprising findings
- Periodicity Injection hurts on Weather, which the authors attribute to weak or imprecise periodicity in natural-phenomenon data.
- Channel-independent single-correlation variant performs worse than the full model, while the data-mixing TSMixer baseline does not surpass CMoS despite far more parameters.
Limitations
- Gains over strongest baselines are small on several datasets (e.g., ETTm1, ETTm2), and some metrics are second-best.
- Theoretical justification is limited to a linear-regression noise-sensitivity argument under Gaussian noise; the authors acknowledge the approach is unvalidated for irregular or random-walk series.
- Periodicity Injection requires dataset-specific period detection via ACF and can degrade performance when periodicity is weak.
Experimental setup
Datasets: Electricity Traffic Weather ETTh1 ETTh2 ETTm1 ETTm2
Benchmarks: Electricity Traffic Weather ETTh1 ETTh2 ETTm1 ETTm2
Metrics: MSE MAE
Baselines: Informer FedFormer TimesNet PatchTST TimeMixer iTransformer DLinear FITS SparseTSF CycleNet
Builds on: DLinear RevIN PatchTST FITS SparseTSF
Closest papers by meaning
- On the Integration of Spatial-Temporal Knowledge: A Lightweight Approach to Atmospheric Time Series Forecasting (NeurIPS 2025 · similarity 0.87)
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.87)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.86)
- How Different from the Past? Spatio-Temporal Time Series Forecasting with Self-Supervised Deviation Learning (NeurIPS 2025 · similarity 0.86)
- Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting (NeurIPS 2025 · similarity 0.86)
- ST-ReP: Learning Predictive Representations Efficiently for Spatial-Temporal Forecasting (AAAI 2025 · similarity 0.85)
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