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Time-o1: Time-Series Forecasting Needs Transformed Label Alignment
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Proposes Time-o1, a model-agnostic loss that projects label sequences onto SVD-derived decorrelated, significance-ranked components and aligns the top components with an L1 loss, reducing label autocorrelation bias and task count.
Problem
Temporal MSE used to train time-series forecasters ignores label autocorrelation, making it a biased likelihood, and its number of tasks grows with the forecast horizon, complicating optimization in long-term forecasting.
Approach
Transform the label sequence with an SVD-derived projection matrix into decorrelated components ranked by variance, then train the forecaster by aligning only the top-K components (L1), fused with the standard MSE loss.
Key results
- On long-term forecasting, Time-o1 achieves best average MSE/MAE on ETTm1 (0.379/0.393), ETTh1 (0.431/0.429), ECL (0.170/0.260) and Traffic (0.419/0.280) among compared models.
- Replacing the MSE loss with Time-o1 on Fredformer reduces ETTh1 MSE by 0.016 (0.447 to 0.431).
- Ablation shows both decorrelation and task reduction components improve over the DF baseline; alpha near 1 and gamma below 1 (e.g., 0.7 on ETTs, 0.3 on Weather) work best.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace TMSE with Time-o1, using significant decorrelated components | Fredformer and dataset-specific baseline models · Long-term forecasting datasets | MSE: 0.016 | Helped |
| reduce the number of tasks using a randomized projection and a subset of components (ablation) | DF · Weather | MAE: -0.012 MAE | Helped |
| align decorrelated components without reducing the number of components (ablation) | DF · ETTm1, ETTh1, ECL, and Weather | MSE: 0.387 -> 0.382; 0.447 -> 0.439; 0.179 -> 0.172; 0.249 -> 0.244 | Helped |
| combine decorrelation with retention of only the most significant components (ablation) | DF · ETTm1, ETTh1, ECL, and Weather | MSE: 0.387 -> 0.379; 0.447 -> 0.431; 0.179 -> 0.170; 0.249 -> 0.241 | Helped |
| use RPCA transformation instead of no transformation (ablation) | Time-o1 training setup · ECL and Weather | MSE: 0.179 -> 0.171; 0.249 -> 0.244 | Helped |
| use SVD transformation instead of no transformation (ablation) | Time-o1 training setup · ECL and Weather | MSE: 0.179 -> 0.175; 0.249 -> 0.248 | Helped |
| use factor analysis instead of no transformation (ablation) | Time-o1 training setup · ECL and Weather | MSE: 0.179 -> 0.175; 0.249 -> 0.245 | Helped |
| increase the transform-loss weight α from 0 to 1 (ablation) | Time-o1 · ETTh2 | MSE: 0.3766 -> 0.3606 | Helped |
| set α to 1 rather than 0.5 (ablation) | Time-o1 · Weather | MSE: 0.2432 -> 0.2753 | Hurt |
| retain all components (γ=1) rather than γ=0.7 (ablation) | Time-o1 · ETTm1 | MSE: 0.3798 -> 0.3814 | Hurt |
Surprising findings
- Retaining all label components (gamma=1) does not yield the best performance; reducing the number of aligned components improves accuracy.
- Shape-alignment losses (Dilate, Soft-DTW, DPTA) give little gain over standard temporal MSE.
Limitations
- Gains are modest on some datasets and horizons (e.g., Weather ablation and some ETTh2 results where baselines are close).
- Autocorrelation estimation relies on double machine learning with linear regression, a specific and approximate estimator.
- Evaluated only on forecasting benchmarks; applicability to speech, detection, or dense prediction is untested.
Experimental setup
Datasets: ETT ECL Traffic Weather PEMS M4
Benchmarks: ETTm1 ETTm2 ETTh1 ETTh2 ECL Traffic Weather PEMS03 PEMS08 M4
Metrics: MSE MAE
Baselines: Fredformer iTransformer FreTS TimesNet MICN TiDE DLinear FEDformer Autoformer Transformer FreDF Koopman
Builds on: FreDF Fredformer iTransformer PCA Dilate
Closest papers by meaning
- FreDF: Learning to Forecast in the Frequency Domain (ICLR 2025 · similarity 0.87)
- Sequence Complementor: Complementing Transformers for Time Series Forecasting with Learnable Sequences (AAAI 2025 · similarity 0.86)
- Time-LLM: Time Series Forecasting by Reprogramming Large Language Models (ICLR 2024 · similarity 0.86)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.86)
- Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts (ICLR 2025 · similarity 0.86)
- TimePerceiver: An Encoder-Decoder Framework for Generalized Time-Series Forecasting (NeurIPS 2025 · similarity 0.86)
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