Research map / Time series / Long-term forecasting
Patch-wise Structural Loss for Time Series Forecasting
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Proposes Patch-wise Structural (PS) loss, combining patch-level correlation, variance (softmax-KL) and mean losses with MSE and gradient-based dynamic weighting, improving five time-series forecasting backbones across seven datasets.
Problem
Point-wise losses such as MSE ignore structural dependencies in time series, failing to capture correlation, variance and mean discrepancies, especially locally in non-stationary series.
Approach
Compare prediction and ground truth at the patch level, with patch length set from the ground truth's dominant Fourier period, using a sum of patch-wise Pearson correlation loss, softmax-KL variance loss and mean MAE loss, added to MSE and balanced by gradient-norm-based dynamic weights.
Key results
- PS loss improves DLinear by average 5.22% MSE and 4.39% MAE reduction, and beats MSE in 134 of 140 long-term forecasting cases.
- In zero-shot forecasting, PS loss beats MSE in 34 of 36 scenarios on ETT datasets (horizon 192).
- PS loss achieves lowest MSE/MAE in most cases versus TILDE-Q and FreDF on iTransformer across ETTh1, ETTm1 and Weather.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PS loss to iTransformer | iTransformer · ETTh1 Avg | MSE: 0.457 -> 0.440 | Helped |
| Add PS loss to iTransformer | iTransformer · ETTh2 Avg | MSE: 0.384 -> 0.375 | Helped |
| Add PS loss to iTransformer | iTransformer · ETTm1 Avg | MSE: 0.408 -> 0.396 | Helped |
| Add PS loss to iTransformer | iTransformer · ETTm2 Avg | MSE: 0.292 -> 0.281 | Helped |
| Add PS loss to iTransformer | iTransformer · Weather Avg | MSE: 0.261 -> 0.253 | Helped |
| Add PS loss to iTransformer | iTransformer · ECL Avg | MSE: 0.176 -> 0.172 | Helped |
| Add PS loss to iTransformer | iTransformer · Exchange Avg | MSE: 0.364 -> 0.366 | Hurt |
| Add correlation loss (ablation) | DLinear + PS · ETTh1 96 | MSE: 0.381 -> 0.367 | Helped |
| Add variance loss (ablation) | DLinear + PS · ETTh1 96 | MSE: 0.380 -> 0.367 | Helped |
| Add mean loss (ablation) | DLinear + PS · ETTh1 96 | MSE: 0.372 -> 0.367 | Helped |
| Use patching rather than processing the full series (ablation) | DLinear + PS · ETTh1 96 | MSE: 0.380 -> 0.367 | Helped |
| Use dynamic weighting rather than fixed weights (ablation) | DLinear + PS · ETTh1 96 | MSE: 0.384 -> 0.367 | Helped |
Surprising findings
- Models trained with PS loss have higher training error but lower test error, which the authors interpret as reduced overfitting.
Limitations
- Overhead grows on large datasets (ECL up to 8.5 s/epoch extra at horizon 720).
- Hyperparameters lambda and delta are tuned per setting; delta matters for datasets where dominant period exceeds threshold.
- Gains are reported on mostly modest margins, and the GDW weighting is heuristic.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Weather ECL Exchange
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Weather ECL Exchange
Metrics: MSE MAE DTW TDI PCC
Baselines: MSE TILDE-Q FreDF iTransformer PatchTST TimeMixer DLinear TimesNet OFA AutoTimes
Builds on: MSE Pearson correlation coefficient GradNorm-style gradient balancing TILDE-Q FreDF
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