# Learning Robust Spectral Dynamics for Temporal Domain Generalization

arXiv: https://arxiv.org/abs/2505.12585 · HTML: https://mlsanity.com/paper/2505.12585/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 51 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 30)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [A Comprehensive Survey on Source-free Domain Adaptation](https://mlsanity.com/paper/2302.11803/) (2023)
- [Continuously Indexed Domain Adaptation](https://mlsanity.com/paper/2007.01807/) (2020)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Temporal Domain Generalization with Drift-Aware Dynamic Neural Networks](https://mlsanity.com/paper/2205.10664/) (2022)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Domain Generalization through Meta-Learning: A Survey](https://mlsanity.com/paper/2404.02785/) (2024)
- [Generalizing to Evolving Domains with Latent Structure-Aware Sequential Autoencoder](https://mlsanity.com/paper/2205.07649/) (2022)
- [Adapting Multi-modal Large Language Model to Concept Drift From Pre-training Onwards](https://mlsanity.com/paper/2405.13459/) (2024)
- [Online Boosting Adaptive Learning under Concept Drift for Multistream Classification](https://mlsanity.com/paper/2312.10841/) (2023)
- [Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems](https://mlsanity.com/paper/2403.12335/) (2024)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Generalizing across Temporal Domains with Koopman Operators](https://mlsanity.com/paper/2402.07834/) (2024)
- [Model Assessment and Selection under Temporal Distribution Shift](https://mlsanity.com/paper/2402.08672/) (2024)
- [Advancing Open-Set Domain Generalization Using Evidential Bi-Level Hardest Domain Scheduler](https://mlsanity.com/paper/2409.17555/) (2024)
- [Foresee What You Will Learn: Data Augmentation for Domain Generalization in Non-stationary Environment](https://mlsanity.com/paper/2301.07845/) (2023)
- [ATFNet: Adaptive Time-Frequency Ensembled Network for Long-term Time Series Forecasting](https://mlsanity.com/paper/2404.05192/) (2024)
- [Early Concept Drift Detection via Prediction Uncertainty](https://mlsanity.com/paper/2412.11158/) (2024)
- [CODA: Temporal Domain Generalization via Concept Drift Simulator](https://mlsanity.com/paper/2310.01508/) (2023)
- [Distributionally Robust Policy Learning under Concept Drifts](https://mlsanity.com/paper/2412.14297/) (2024)
- [Towards a theory of learning dynamics in deep state space models](https://mlsanity.com/paper/2407.07279/) (2024)
- [CORAL: Concept Drift Representation Learning for Co-evolving Time-series](https://mlsanity.com/paper/2501.01480/) (2025)
- [Evolving Multi-Scale Normalization for Time Series Forecasting under Distribution Shifts](https://mlsanity.com/paper/2409.19718/) (2024)

## Built on by (most cited first, 14 of 14)

- [Drift-aware Collaborative Assistance Mixture of Experts for Heterogeneous Multistream Learning](https://mlsanity.com/paper/2508.01598/) (2025)
- [Generalized Incremental Learning under Concept Drift across Evolving Data Streams](https://mlsanity.com/paper/2506.05736/) (2025)
- [See, Plan, Rewind: Progress-Aware Vision-Language-Action Models for Robust Robotic Manipulation](https://mlsanity.com/paper/2603.09292/) (2026)
- [VGAS: Value-Guided Action-Chunk Selection for Few-Shot Vision-Language-Action Adaptation](https://mlsanity.com/paper/2602.07399/) (2026)
- [Bayesian Ego-graph Inference for Networked Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2509.16606/) (2025)
- [Bandwidth-constrained Variational Message Encoding for Cooperative Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2512.11179/) (2025)
- [TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series](https://mlsanity.com/paper/2602.22520/) (2026)
- [DeepBooTS: Dual-Stream Residual Boosting for Drift-Resilient Time-Series Forecasting](https://mlsanity.com/paper/2511.06893/) (2025)
- [Parameter-Efficient Temporal Domain Generalization](https://mlsanity.com/paper/2602.11965/) (2026)
- [Autonomous Drift Learning in Data Streams: A Unified Perspective](https://mlsanity.com/paper/2605.01295/) (2026)
- [Respecting Modality Gap in Post-hoc Out-of-distribution Detection with Pre-trained Vision-Language Models](https://mlsanity.com/paper/2605.26661/) (2026)
- [FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2608.22224/) (2026)
- [Hierarchical Wasserstein Merging for Multi-Domain Multi-Task Learning: From Specialists to a Generalist](https://mlsanity.com/paper/2609.06406/) (2026)
- [Adaptive Spectral-Koopman Dynamics Modeling for Temporal Domain Generalization](https://mlsanity.com/paper/2610.02822/) (2026)

## Abstract (arXiv)

Modern machine learning models struggle to maintain performance in dynamic environments where temporal distribution shifts, i.e., concept drift, are prevalent. Temporal Domain Generalization (TDG) seeks to enable model generalization across evolving domains, yet existing approaches typically assume smooth incremental changes, struggling with complex real-world drifts involving long-term structure (incremental evolution/periodicity) and local uncertainties. To overcome these limitations, we introduce FreKoo, which tackles these challenges via a novel frequency-domain analysis of parameter trajectories. It leverages the Fourier transform to disentangle parameter evolution into distinct spectral bands. Specifically, low-frequency component with dominant dynamics are learned and extrapolated using the Koopman operator, robustly capturing diverse drift patterns including both incremental and periodicity. Simultaneously, potentially disruptive high-frequency variations are smoothed via targeted temporal regularization, preventing overfitting to transient noise and domain uncertainties. In addition, this dual spectral strategy is rigorously grounded through theoretical analysis, providing stability guarantees for the Koopman prediction, a principled Bayesian justification for the high-frequency regularization, and culminating in a multiscale generalization bound connecting spectral dynamics to improved generalization. Extensive experiments demonstrate FreKoo's significant superiority over SOTA TDG approaches, particularly excelling in real-world streaming scenarios with complex drifts and uncertainties.