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SIN: Selective and Interpretable Normalization for Long-Term Time Series Forecasting
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Proposes SIN, a PLS-SVD-based learned normalization that selects statistics maximizing covariance between look-back and future windows, and plugs it into Informer, Autoformer and FEDformer for long-term forecasting.
Problem
Heuristic normalization (e.g., mean shifting, RevIN) for non-stationary time series forecasting does not account for which statistics are appropriate to remove and restore.
Approach
Identify local invariance and global variability as properties of good normalization statistics, then learn linear projections on look-back and future windows by maximizing their covariance via PLS-SVD; mean shifting and DCT are special cases.
Key results
- Autoformer on Traffic improves from 0.615 MSE to 0.539 with SIN (about 12.3%), and FEDformer improves from 0.605 to 0.519 (14.2%).
- On Exchange-Rate, SIN brings all models to around 0.45 MSE, a 72% improvement for Informer.
- Compared with RevIN on FEDformer, SIN gives clearly lower MSE on seasonal datasets (e.g., Traffic horizon 96: 0.493 vs 0.609) and is similar on trend datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add SIN normalization | FEDformer · ETTh1 | MSE: 0.432 -> 0.432 | No clear effect |
| Add SIN normalization | FEDformer · ETTm1 | MSE: 0.438 -> 0.392 | Helped |
| Add SIN normalization | FEDformer · PEMS03 | MSE: 0.184 -> 0.170 | Helped |
| Add SIN normalization | FEDformer · PEMS04 | MSE: 0.141 -> 0.130 | Helped |
| Add SIN normalization | FEDformer · PEMS07 | MSE: 0.144 -> 0.135 | Helped |
| Add SIN normalization | FEDformer · PEMS08 | MSE: 0.271 -> 0.261 | Helped |
| Add SIN normalization | FEDformer · Electricity | MSE: 0.209 -> 0.183 | Helped |
| Add SIN normalization | FEDformer · Exchange-Rate | MSE: 0.506 -> 0.448 | Helped |
| Add SIN normalization | FEDformer · Solar | MSE: 0.353 -> 0.263 | Helped |
| Add SIN normalization | FEDformer · Traffic | MSE: 0.605 -> 0.519 | Helped |
| Add SIN normalization | FEDformer · Weather | MSE: 0.453 -> 0.286 | Helped |
| Replace RevIN with SIN normalization | FEDformer · Traffic (H=96) | MSE: 0.609 -> 0.493 | Helped |
Surprising findings
- Mean shifting, the dominant heuristic, is only the top singular direction for trended series and contributes little covariance on seasonal series like Traffic.
Limitations
- Linear projection in the core formulation; nonlinear extension is only suggested, not evaluated.
- Gains on trended datasets over RevIN are negligible (Exchange-Rate horizons 192-720 are mixed).
Experimental setup
Datasets: ETT Traffic Electricity Exchange-Rate Weather ILI Solar-Energy PEMS
Benchmarks: ETTh1 ETTm1 PEMS03 PEMS04 PEMS07 PEMS08 Electricity Exchange Solar Traffic Weather
Metrics: MSE MAE
Baselines: Informer Autoformer FEDformer RevIN mean shifting
Builds on: RevIN Non-stationary Transformers FEDformer Autoformer Informer
Closest papers by meaning
- DDN: Dual-domain Dynamic Normalization for Non-stationary Time Series Forecasting (NeurIPS 2024 · similarity 0.87)
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