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Generalizing across Temporal Domains with Koopman Operators
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Proposes Temporal Koopman Networks (TKNets), which learn a Koopman operator in a measurement-function embedding space to forecast the next domain's class-conditional centroids, backed by a generalization bound tied to a λ-consistency notion for temporal domain generalization.
Problem
Generalizing a classifier to an unseen future target domain without target data when the source domains evolve over time (temporal domain generalization), where existing DG methods treat domains as exchangeable.
Approach
Model the evolution between consecutive domains as a linear Koopman operator acting on learned measurement functions, forecast class centroids for the next domain from the support set, and train with a prototype-style episodic loss; theory shows aligning class-conditional distributions of forecasted and real domains tightens the target risk bound.
Key results
- TKNets achieves 85.7% average accuracy across six datasets, versus 83.3% for the next best method GI and 74.7% for ERM.
- On RMNIST with 15 domains and the last four as targets, TKNets reaches 72.2% at T+4 while other methods drop to 41.0-44.1%.
- TKNets reaches 94.2% on EvolCircle and 95.0% on RPlate, compared with 72.7% and 63.9% for ERM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use TKNets instead of GI | Temporal domain generalization · EvolCircle | accuracy (%): 92.1 $\pm$ 1.7 -> 94.2 $\pm$ 0.9 | Helped |
| use TKNets instead of GI | Temporal domain generalization · RPlate | accuracy (%): 94.3 $\pm$ 0.4 -> 95.0 $\pm$ 0.5 | Helped |
| use TKNets instead of CIDA | Temporal domain generalization · RMNIST | accuracy (%): 86.5 $\pm$ 1.2 -> 87.5 $\pm$ 0.1 | Helped |
| use TKNets instead of Mixup | Temporal domain generalization · Portrait | accuracy (%): 96.4 $\pm$ 0.2 -> 97.2 $\pm$ 0.0 | Helped |
| use TKNets instead of ERM | Temporal domain generalization · Cover Type | accuracy (%): 71.8 $\pm$ 0.2 -> 73.8 $\pm$ 1.0 | Helped |
| use TKNets instead of CIDA | Temporal domain generalization · FMoW | accuracy (%): 63.4 $\pm$ 0.2 -> 66.8 $\pm$ 0.1 | Helped |
| use learned rather than predefined measurement functions (ablation) | TKNets · RMNIST | accuracy (%): 86.6 $\pm$ 0.2 -> 87.5 $\pm$ 0.1 | Helped |
| use predefined rather than learned measurement functions (ablation) | TKNets · Portrait | accuracy (%): 96.4 $\pm$ 0.0 -> 97.2 $\pm$ 0.0 | Helped |
| use predefined rather than learned measurement functions (ablation) | TKNets · Cover Type | accuracy (%): 72.5 $\pm$ 0.8 -> 73.8 $\pm$ 1.0 | Helped |
| incorporate domain index as a one-dimension feature (ablation) | ERM · EvolCircle | accuracy (%): 72.7 $\pm$ 1.1 -> 73.6 $\pm$ 0.6 | No clear effect |
| incorporate domain index as a one-hot feature (ablation) | ERM · RPlate | accuracy (%): 63.9 $\pm$ 0.9 -> 64.0 $\pm$ 0.3 | No clear effect |
Surprising findings
- Incorporating domain index information into ERM yields only marginal gains, suggesting that index information alone does not capture the evolving pattern.
- Traditional DG methods' performance on RMNIST fluctuates or does not improve as the number of source domains increases, whereas TKNets improves.
Limitations
- The λ-consistency term is unobservable and the bound depends on the KL between forecasted and real conditional distributions, which cannot be computed on the target domain.
- Gains over baselines are reported on relatively small or synthetic benchmarks (e.g., RMNIST with 200 samples per domain).
- Performance on source domains may be lower than ERM, since the model focuses on forecasting the target domain.
Experimental setup
Datasets: EvolCircle RPlate RMNIST Portrait Cover Type FMoW
Benchmarks: EvolCircle RPlate RMNIST Portrait Cover Type FMoW
Metrics: accuracy
Baselines: ERM GroupDRO MLDG MMD SagNet VREx SD IRM Mixup CORAL MTL RSC
Builds on: Koopman theory DomainBed prototypical networks CIDA GI
Closest papers by meaning
- Continuous Temporal Domain Generalization (NeurIPS 2024 · similarity 0.94)
- Learning Robust Spectral Dynamics for Temporal Domain Generalization (NeurIPS 2025 · similarity 0.89)
- Learning Time-Aware Causal Representation for Model Generalization in Evolving Domains (ICML 2025 · similarity 0.88)
- Enhancing Evolving Domain Generalization through Dynamic Latent Representations (AAAI 2024 · similarity 0.88)
- Continuous Domain Generalization (NeurIPS 2025 · similarity 0.87)
- Weight Diffusion for Future: Learn to Generalize in Non-Stationary Environments (NeurIPS 2024 · similarity 0.86)
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