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Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting
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Proposes ST-TTC, a test-time computing paradigm for spatio-temporal forecasting that trains a lightweight frequency-domain calibrator (per-node, grouped amplitude/phase offsets) with single-step flash gradient updates on delayed-label samples held in a streaming FIFO queue, with the backbone frozen.
Problem
Spatio-temporal forecasting degrades under non-stationary periodic shifts, noise and distribution shift at deployment; existing robustness methods need costly retraining or architecture changes, and prior test-time methods (TTT-ST, DOST) are complex and too slow for the per-step timeliness requireme
Approach
Append a lightweight spectral-domain calibrator that applies learnable per-group, per-node amplitude and phase offsets to the backbone's rFFT output, updated online with one gradient step per test sample using labels of historical samples dequeued from a FIFO memory queue (delayed by the horizon to avoid leakage), while the backbone stays frozen.
Key results
- Applying ST-TTC to six backbones (STAEformer, STTN, GWNet, STGCN, STID, ST-Norm) reduces MAE across six datasets, e.g. about 1-2% on PEMS-03 and up to ~2.4% MAPE gains, with consistent improvements.
- On METR-LA in the online setting (20% train split), ST-TTC reports MAE 3.77 vs. DOST 4.38 and OneNet 4.94, without modifying the backbone.
- On continual learning (Energy-Stream), ST-TTC with EAC reduces MAE from 5.15 to 3.47 (about 32.6%), and in the OOD setting gains grow with node shift.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add ST-TTC calibration to forecasting backbones | Spatio-temporal forecasting models · PEMS-03, PEMS-04, PEMS-07, PEMS-08, KnowAir, and UrbanEV | MAE: GWNet on PEMS-03: 16.73 ±0.41 -> 16.42 ±0.19; STAEformer on PEMS-04: 19.48 ±0.05 -> 19.33 ±0.06; STAEformer on PEMS-07: | Helped |
| Add ST-TTC to EAC | EAC · Air-Stream, PEMS-Stream, and Energy-Stream | MAE: Air-Stream: 24.15 ±0.14 -> 23.54 ±0.15; PEMS-Stream: 14.92 ±0.11 -> 14.71 ±0.07; Energy-Stream: 5.15 ±0.10 -> 3.47 ±0.01 | Helped |
| Add ST-TTC to STKEC | STKEC · Air-Stream, PEMS-Stream, and Energy-Stream | MAE: Air-Stream: 25.44 ±1.05 -> 24.26 ±0.05; PEMS-Stream: 16.25 ±0.04 -> 16.05 ±0.06; Energy-Stream: 5.41 ±0.15 -> 3.83 ±0.09 | Helped |
| Use frequency-domain rather than nonlinear time-domain calibration (ablation) | ST-TTC · OOD setting with 20% new nodes | forecasting performance | Helped |
| Add amplitude modulation (ablation) | ST-TTC spectral calibrator · OOD setting with 20% new nodes | forecasting performance | Helped |
| Use node-specific rather than shared-node calibration (ablation) | ST-TTC spectral calibrator · OOD setting with 20% new nodes | forecasting performance | Helped |
| Select recent samples rather than random samples for updates (ablation) | ST-TTC update strategy · OOD setting with 20% new nodes | forecasting performance | Helped |
| Retrieve the most similar samples instead of using the proposed update strategy (ablation) | ST-TTC update strategy · OOD setting with 20% new nodes | forecasting performance | No clear effect |
| Increase the learning rate (ablation) | ST-TTC · OOD setting with 20% new nodes | forecasting performance | Hurt |
| Use fewer frequency groups (ablation) | ST-TTC spectral calibrator · OOD setting with 20% new nodes | forecasting performance | Hurt |
| Increase the number of update samples or update steps (ablation) | ST-TTC · OOD setting with 20% new nodes | forecasting performance: fluctuations < 1% | No clear effect |
Surprising findings
- Amplitude modulation is the main contributor to gains, and sharing calibration parameters across nodes degrades performance due to spatial heterogeneity.
- Retrieving similar historical samples gives negligible gains while adding computational cost, and increasing the number of update samples or steps has minimal effect on accuracy.
Limitations
- Theoretical perturbation bound and convergence result rely on linearized approximations and assumptions (Lipschitz gradients, bounded gradients) that are not verified empirically.
- Comparisons with CompFormer and DOST use reported numbers because their code is unavailable, and TTT-ST is replaced by TTT-MAE, making some comparisons unfair or indirect.
Experimental setup
Datasets: PEMS-03 PEMS-04 PEMS-07 PEMS-08 KnowAir UrbanEV METR-LA ST (LargeST: SD, GBA, GLA, CA) Air-Stream PEMS-Stream Energy-Stream
Benchmarks: PEMS-03 PEMS-04 PEMS-07 PEMS-08 KnowAir UrbanEV METR-LA LargeST Air-Stream PEMS-Stream Energy-Stream
Metrics: MAE RMSE MAPE
Baselines: TTT-MAE TENT OnlineTCN FSNet OneNet CompFormer DOST STONE EAC STKEC PatchSTG
Builds on: test-time training TENT STONE EAC
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