Research map / Time series / Long-term forecasting
AliO: Output Alignment Matters in Long-Term Time Series Forecasting
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Proposes AliO, a loss that aligns LTSF model predictions for overlapping timestamps across lagged inputs (time and frequency domains with regression pulling), and a new metric TAM to quantify output alignment.
Problem
Long-term time series forecasters produce inconsistent predictions for the same timestamps when fed lagged input windows, undermining reliability; existing metrics like MSE only measure distance to ground truth.
Approach
AliO adds a loss that pulls overlapping predictions from lagged inputs toward each other in time and frequency domains, using stop-gradient "regression pulling" so the alignment direction agrees with the regression loss; TAM measures MAE between overlapping prediction pairs.
Key results
- AliO improves TAM by up to 70.5% for CycleNet and up to 64.0% for DLinear on the main datasets, while MSE improves by up to 11.5% on those datasets.
- On ILI, AliO yields 17.4% MSE improvement and 58.1% TAM improvement relative to baselines.
- Abstract reports up to 58.2% TAM improvement and up to 27.5% forecasting performance improvement across models and datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add AliO to DLinear | DLinear · ECL, ETTh1, ETTh2, ETTm1, ETTm2, Traffic, Weather | TAM₂ | Helped |
| Add AliO to DLinear | DLinear · ECL, ETTh1, ETTh2, ETTm1, ETTm2, Traffic, Weather | MSE | Helped |
| Add AliO to PatchTST | PatchTST · ILI | MSE: 1.813 -> 1.497 | Helped |
| Add AliO to PatchTST | PatchTST · ILI | TAM₂: 0.110 -> 0.046 | Helped |
| Add AliO to TimesNet | TimesNet · ILI | MSE: 2.176 -> 1.963 | Helped |
| Add AliO to TimesNet | TimesNet · ILI | TAM₂: 0.322 -> 0.258 | Helped |
| Add AliO to DLinear | DLinear · ILI | MSE: 2.247 -> 2.187 | Helped |
| Add AliO to DLinear | DLinear · ILI | TAM₂: 0.152 -> 0.119 | Helped |
| Increase the number of overlapping output sequences N (ablation) | AliO · LTSF datasets | TAM | Helped |
| Increase lag l (ablation) | AliO · LTSF datasets | TAM | Hurt |
| Increase time-domain coefficient λT (ablation) | AliO · LTSF datasets | TAM | Helped |
| Vary frequency-domain coefficient λF (ablation) | AliO · LTSF datasets | TAM: 0.50 | Mixed |
Surprising findings
- Increasing the time-domain alignment coefficient improved normalized MSE as well as TAM, suggesting regression pulling aligns the AliO loss with the regression loss.
- Higher initial TAM (poorer alignment) correlates with larger MSE gains from AliO (correlation coefficient 0.33).
Limitations
- TAM may be unreliable on highly volatile datasets or under sudden out-of-distribution events.
- AliO gains are smaller when initial alignment is already good; MSE distance function may limit improvements.
- Hyperparameter search over lambda_T and lambda_F and window settings (N, l) is needed.
Experimental setup
Datasets: ECL ETTh1 ETTh2 ETTm1 ETTm2 Traffic Weather ILI
Benchmarks: ECL ETTh1 ETTh2 ETTm1 ETTm2 Traffic Weather ILI
Metrics: MSE MAE MAPE RMSE TAM
Baselines: CycleNet GPT4TS iTransformer PatchTST TimesNet DLinear Autoformer
Builds on: DLinear PatchTST iTransformer TimesNet CycleNet
Closest papers by meaning
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.87)
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.86)
- Align-RAG: Alignment Is All You Need for TSFM In-Context Learning (NeurIPS 2026 · similarity 0.85)
- Time-o1: Time-Series Forecasting Needs Transformed Label Alignment (NeurIPS 2025 · similarity 0.85)
- SEMPO: Lightweight Foundation Models for Time Series Forecasting (NeurIPS 2025 · similarity 0.85)
- ARM: Refining Multivariate Forecasting with Adaptive Temporal-Contextual Learning (ICLR 2024 · similarity 0.84)
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