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Learning Robust Spectral Dynamics for Temporal Domain Generalization
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Proposes FreKoo, which Fourier-decomposes parameter trajectories across temporal domains, extrapolates low-frequency components with a learned Koopman operator, and smooths high-frequency components with a temporal regularizer, evaluated on seven TDG benchmarks.
Problem
Temporal domain generalization under concept drift that combines long-term incremental/periodic dynamics with domain-specific local uncertainties that cause overfitting.
Approach
Treat model parameter trajectories across time as signals; split them via DFT into low-frequency dominant dynamics (extrapolated by a learnable linear Koopman operator in latent space) and high-frequency components (regularized by a temporal smoothness penalty, interpreted as a Gaussian random-walk MAP prior), and predict the next-domain parameters from both.
Key results
- FreKoo reports the best error on 2-Moons (1.0±0.3%), Rot-MNIST (6.9±0.7%), ONP (32.3±0.3%), Shuttle (0.20±0.02%), Elec2 (9.2±0.7%) and Appliance MAE (4.0±0.1), outperforming prior TDG baselines such as Koodos and DRAIN.
- On the House Prices regression benchmark FreKoo (9.0 MAE) is second to Koodos (8.8), which the paper highlights as the one dataset it does not lead.
- Ablation removing the Koopman operator raises 2-Moons error from 1.0% to 15.3% and Elec2 error from 9.2% to 28.9%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the Koopman operator (ablation) | FreKoo · 2-Moons | misclassification error (%): 15.3 $\pm $ 1.7 -> 1.0 $\pm$ 0.3 | Helped |
| add the Koopman operator (ablation) | FreKoo · Elec2 | misclassification error (%): 28.9 $\pm$ 2.4 -> 9.2 $\pm$ 0.7 | Helped |
| add the Koopman operator (ablation) | FreKoo · Appliance | MAE: 9.4 $\pm$ 0.7 -> 4.0 $\pm$ 0.1 | Helped |
| add frequency decomposition (ablation) | FreKoo · 2-Moons | misclassification error (%): 2.6 $\pm $ 0.8 -> 1.0 $\pm$ 0.3 | Helped |
| add frequency decomposition (ablation) | FreKoo · Elec2 | misclassification error (%): 14.2 $\pm$ 1.9 -> 9.2 $\pm$ 0.7 | Helped |
| add frequency decomposition (ablation) | FreKoo · Appliance | MAE: 5.2 $\pm$ 0.4 -> 4.0 $\pm$ 0.1 | Helped |
| add parameter reconstruction loss (ablation) | FreKoo · 2-Moons | misclassification error (%): 9.1 $\pm$ 1.7 -> 1.0 $\pm$ 0.3 | Helped |
| add parameter reconstruction loss (ablation) | FreKoo · Elec2 | misclassification error (%): 12.2 $\pm$ 1.0 -> 9.2 $\pm$ 0.7 | Helped |
| add parameter reconstruction loss (ablation) | FreKoo · Appliance | MAE: 4.3 $\pm$ 0.4 -> 4.0 $\pm$ 0.1 | Helped |
| add Koopman consistency loss (ablation) | FreKoo · 2-Moons | misclassification error (%): 6.7 $\pm$ 0.9 -> 1.0 $\pm$ 0.3 | Helped |
| add Koopman consistency loss (ablation) | FreKoo · Elec2 | misclassification error (%): 10.0 $\pm$ 0.8 -> 9.2 $\pm$ 0.7 | Helped |
| add Koopman consistency loss (ablation) | FreKoo · Appliance | MAE: 4.2 $\pm$ 0.6 -> 4.0 $\pm$ 0.1 | Helped |
Surprising findings
- The ablation removing the high-frequency regularizer R_high gives a lower 2-Moons error (2.3%) than the full-model variant with no change? In practice removing R_high raises Elec2 error from 9.2% to 10.5%, while removing the frequency decomposition (w/o Freq.) lowers 2-Moons error to 2.6% relative t
Limitations
- Frequency-separation threshold (energy preservation ratio tau) is a fixed heuristic chosen by the authors, as acknowledged in future work.
- The generalization bound relies on strong assumptions (Lipschitz encoders/decoder, bounded Rademacher complexity) and the proof's estimation-error step is loosely argued.
- Evaluation is limited to small-scale benchmarks with simple base models; the method is not tested on large neural networks or online streams.
Experimental setup
Datasets: Rotated 2-Moons Rotated MNIST Online News Popularity Shuttle Electrical Demand (Elec2) House Prices Appliances Energy Prediction
Benchmarks: Rotated 2-Moons Rotated MNIST ONP Shuttle Elec2 House Prices Appliances Energy P-Moons (37-domain periodic extension)
Metrics: misclassification error (%) mean absolute error (MAE)
Baselines: Offline LastDomain IncFinetune CDOT CIDA GI LSSAE DDA DRAIN EvoS Koodos
Builds on: Koopman operator theory CDOT DRAIN
Closest papers by meaning
- Continuous Temporal Domain Generalization (NeurIPS 2024 · similarity 0.90)
- Generalizing across Temporal Domains with Koopman Operators (AAAI 2024 · similarity 0.89)
- ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals (ICML 2025 · similarity 0.86)
- Continuous Domain Generalization (NeurIPS 2025 · similarity 0.86)
- Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators (NeurIPS 2026 · similarity 0.85)
- Out-of-Domain Generalization in Dynamical Systems Reconstruction (ICML 2024 · similarity 0.85)
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