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REVIEW 3 major objections 5 minor 48 references

Learning Robust Spectral Dynamics for Temporal Domain Generalization

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Splitting parameter drift into predictable low frequencies and noisy high frequencies gives state-of-the-art temporal domain generalization.

desk verdict Novel spectral-Koopman combination for TDG with solid empirical promise, but Theorem 1's proof implicitly needs target-domain samples and the theoretical grounding is vacuous. read the letter →

arxiv 2505.12585 v1 pith:PXYN4DCT submitted 2025-05-19 cs.LG cs.AI

En Yu , Jie Lu , Xiaoyu Yang , Guangquan Zhang , Zhen Fang This is my paper · ORCID
classification cs.LGcs.AI
keywords temporaldomaingeneralizationconceptdriftparametertrajectorypredictionFourierspectraldecompositionKoopmanoperatorfrequency-domainlearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

FreKoo claims that a model's parameter trajectory over time, not just its data, carries the signal needed to generalize to future domains, and that this signal is spectrally separated: long-term incremental and periodic drift concentrates at low frequencies, while transient noise and domain-specific artifacts concentrate at high frequencies. The paper builds a training procedure that decomposes parameter trajectories with a Fourier mask, models the low-frequency part with a learned Koopman operator for stable linear extrapolation, and regularizes the high-frequency part toward smoothness instead of trying to predict it. It proves a multiscale generalization bound in which the excess risk on the future target domain is controlled by the latent prediction errors of the two spectral bands, plus a standard sample-complexity term. On seven temporal-domain-generalization benchmarks spanning synthetic rotations and real-world streams, the method reports the best error on six, with the largest gains on periodic-drift datasets. A sympathetic reader would take the paper's contribution to be a proof of concept that frequency-domain dynamics of parameters is a usable inductive bias for robust temporal generalization.

What carries the argument

The central machinery is the spectral decomposition of the parameter trajectory $\Theta = [\theta_1,\dots,\theta_T]$ via a temporal discrete Fourier transform. An energy proxy averages spectral magnitudes across parameter dimensions, a binary mask keeps the top-$Q$ frequencies ($Q = \lceil \tau N_{\text{freq}} \rceil$), and inverse DFT splits $\Theta$ into $\Theta_{\text{low}} + \Theta_{\text{high}}$. The low-frequency part feeds an encoder $\phi_{\text{low}}$ into a latent space where a learnable matrix $K$ approximates the Koopman operator and propagates $z_{t,\text{low}}$ linearly, with a reconstruction loss enforcing consistency; the high-frequency part feeds a separate encoder and is penalized by $\sum_{t} \|z_{t+1,\text{high}} - z_{t,\text{high}}\|^2$, equivalent to MAP estimation under a random-walk prior. The predicted next parameters are $\phi^{-1}(K\phi_{\text{low}}(\theta_{t,\text{low}}) + \phi_{\text{high}}(\theta_{t,\text{high}}))$. This construction carries the argument: $K$'s Jordan structure bounds low-frequency extrapolation error, the regularizer controls high-frequency bias, and Theorem 1 chains both to target-domain excess risk.

What would settle it

Construct a parameter trajectory that is a strong low-frequency sinusoid plus a weak linear drift whose frequency bin falls below the energy threshold, train FreKoo with $\tau$ chosen to mask that bin, and test on the continuation; if the predicted $\theta_{T+1}$ errors are no better than a method that forecasts all frequencies, the spectral-separation hypothesis is falsified. The same test can be run on real streams by computing oracle optimal parameters of future test domains and measuring the Fourier energy of their difference trajectory in the masked bins.

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Extended reading notes

Core claim

The central claim is that temporal domain generalization reduces to predicting the next point of a parameter trajectory, and that this prediction is made reliable by separating the trajectory into a predictable low-frequency component and a noisy high-frequency component. FreKoo selects the dominant Fourier bins by average spectral magnitude, keeps those as $\Theta_{\text{low}}$ and models their evolution with a linear Koopman operator $K$ in a learned latent space, while the residual $\Theta_{\text{high}}$ is not extrapolated but constrained by a temporal-difference regularizer equivalent to a Gaussian random-walk prior. The predicted parameter for the next domain is decoded from the sum of the Koopman-extrapolated low-frequency latent and the regularized high-frequency latent. The theory states that the excess risk on the target domain is bounded by Lipschitz constants times $(E_{\text{low}} + E_{\text{high}})$ plus a Rademacher-complexity term, where $E_{\text{low}}$ is controlled by Koopman stability and $E_{\text{high}}$ by the smoothness regularizer; experiments report state-of-the-art error on six of seven benchmarks, with clear gains where drift is periodic or noisy.

Load-bearing premise

The load-bearing premise is that the future-relevant part of parameter drift, including incremental trends and recurring cycles, occupies the few strongest Fourier frequencies selected by the energy mask, while everything discarded as high-frequency is transient noise; if real signal lives in the masked-out bins, the method both fails to extrapolate it and actively smooths it away.

Editorial extensions

If this is right

  • On benchmarks with recurring seasonal drift (Elec2 and Appliance energy), the method reports errors of 9.2% and 4.0 MAE, substantially below prior temporal domain generalization baselines, so periodicity does not have to be detected explicitly to be exploited.
  • Because the generalization bound is additive in $E_{\text{low}}$ and $E_{\text{high}}$, any future method that reduces either latent error directly improves the target-domain guarantee.
  • The frequency decomposition is applied to parameters rather than data, so the framework can be attached to any base model whose parameters are trained sequentially on ordered domains.
  • The ablation shows that removing the Koopman term degrades 2-Moons error from 1.0% to 15.3% and Elec2 from 9.2% to 28.9%, indicating the linear low-frequency extrapolation is the main driver of the gains.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the spectral-separation hypothesis implies a testable diagnostic—compute the oracle optimal parameters for future test domains and check whether their Fourier energy lies in the masked low-frequency bins; if it does not, no amount of Koopman tuning can rescue the mask.
  • The paper leaves the threshold $\tau$ as a fixed hyperparameter; a natural extension is to learn $\tau$ per dimension or per dataset from a validation future domain, since the sensitivity analysis shows the optimal value differs between 2-Moons (higher better) and Appliance (intermediate).
  • If concept drift contains sudden regime shifts, those shifts appear as broad-spectrum energy and will be partially smoothed away by the high-frequency regularizer; a testable extension is to compare FreKoo against detect-then-adapt methods on sudden-drift streams, where the method's assumptions are least favorable.
  • Another implication is that the parameter trajectory itself becomes a learned representation: after training, $\Theta_{\text{low}}$ can be inspected as a spectral signature of the environment, helping practitioners distinguish periodic market or usage cycles from noise in deployed models.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes FreKoo, a method for temporal domain generalization (TDG) that analyzes the trajectory of model parameters in the frequency domain. It decomposes the parameter trajectory into low-frequency and high-frequency components via a discrete Fourier transform, models the low-frequency dynamics with a learned Koopman operator, and applies a smoothness regularization to the high-frequency components. The authors claim a novel multiscale generalization bound (Theorem 1) that connects the spectral decomposition, Koopman stability, and high-frequency regularization to target-domain excess risk. They report state-of-the-art results on six of seven TDG benchmarks, with additional experiments on periodicity modeling, ablations, and sensitivity analysis.

Significance. If valid, the frequency-domain perspective on parameter trajectories would be a meaningful contribution to TDG, offering a principled way to separate predictable drift from noise. The framework is novel and the experimental design covers a diverse set of drift types. However, the theoretical centerpiece, Theorem 1, is derived in a setting that is incompatible with the problem definition, and the bound is expressed in terms of unquantified errors. The empirical superiority is also not uniformly supported: on House the method is worse than Koodos, and on Rot-MNIST the difference is within one standard deviation. The method itself may have merit, but the central claims as presented are not established.

major comments (3)
  1. [Section 3.3 / Appendix B.4, Eq. (37)] The proof of Theorem 1 bounds the true target risk by an empirical risk E_n[l(g(X;θ̂_{T+1}),Y)] plus O(1/√n), where E_n is over n samples drawn from the target domain D_{T+1}. In the TDG setting, D_{T+1} is an unseen future domain and no target samples are available during training. Therefore E_n is undefined, the probability statement over draws from D_{T+1} is vacuous, and the theorem does not establish any bound on the expected excess risk for the actual target domain. This is not a minor gap in constants; it removes the claimed connection between FreKoo's spectral-Koopman mechanism and improved target generalization.
  2. [Section 3.3 / Appendix B.2, B.3, Eq. (12)] The bound in Eq. (12) contains the terms Elow and Ehigh, but these are not bounded by the stated lemmas. Lemma 1 only bounds the propagation of an initial error under K; it does not bound the initial error itself, and no training constraint enforces ρ(K)<1. Lemma 2 establishes an equivalence between Rhigh and a Gaussian random-walk MAP estimate, but provides no bound on Ehigh. Consequently, the first term of the bound is unquantified, and the theorem does not yield a finite generalization guarantee for the proposed objective.
  3. [Assumption 2 / Eq. (15) and Appendix B.4] The Rademacher complexity bound in Assumption 2 is assumed for sequences drawn from the target domain D_{T+1}. As in the first major comment, this assumption references an inaccessible quantity in TDG, and the proof does not justify how a bound on source-domain complexity transfers to the target. Moreover, the estimation error term in the proof is asserted as a 'standard' bound without formal treatment of the β-mixing assumption or a clear derivation from the stated Rademacher bound to the specific predictor θ̂_{T+1}.
minor comments (5)
  1. [Section 3.3, Lemma 2] The claim of a 'principled Bayesian justification' for Rhigh is overstated: Lemma 2 merely restates the Tikhonov form of the regularizer as a Gaussian random-walk prior, which is an equivalence, not an independent justification.
  2. [Table 1] The claim of state-of-the-art performance on six of seven benchmarks is not fully supported: on House, FreKoo (9.0 MAE) is worse than Koodos (8.8), and on Rot-MNIST the difference between FreKoo (6.9±0.7) and Koodos (7.0±0.3) is within one standard deviation. The authors should provide statistical significance tests or a more nuanced discussion.
  3. [Eq. (9)] There is a punctuation error in Eq. (9): the expression ends with a period instead of a closing parenthesis, and the opening parenthesis in the argument of φ^{-1} is not closed.
  4. [Section 4.4] The P-Moons dataset used for the periodicity experiment is not formally defined in the main text; it appears to be the 37-domain extended 2-Moons benchmark, but this should be stated explicitly before presenting the results.
  5. [Section 2 / Appendix A] The related-work section mentions several references that are not cited in the main text (e.g., Refs. [36]-[38] are only used in Appendix A). It would improve readability to either cite them in the main text or consolidate the related-work appendix.

Circularity Check

2 steps flagged · score 4.0 of 10

Two steps of the theoretical derivation reduce to their own definitions: Lemma 2's "Bayesian justification" is the regularizer restated under a Gaussian random-walk prior, and Theorem 1's generalization bound requires samples from the unseen target domain; the empirical evaluation itself is independent.

  1. self definitional [Section 3.3, Lemma 2; proof in Appendix B.3; regularizer defined in Eq. (8).]
    "Lemma 2 (High-Frequency Smoothness Bias) Minimising Rhigh is equivalent to maximum-a-posteriori estimation the Gaussian random-walk prior zt+1,high = zt,high + ξt, ξt∼N(0,σ²I), with precision λ = 1/(2σ²). ... Therefore, minimizing Rhigh is equivalent to minimizing 1/(2σ²)Rhigh, since 1/(2σ²) is a positive constant. This shows that minimizing Rhigh is equivalent to MAP estimation under the specified Gaussian random-walk prior with precision λprior = 1/(2σ²)."

    The regularizer Rhigh is defined as Σ∥z_{t+1,high}−z_{t,high}∥². The Gaussian random-walk prior is chosen with transition z_{t+1,high}=z_{t,high}+ξ_t, ξ_t∼N(0,σ²I), whose negative log-density is exactly (1/2σ²)∥z_{t+1,high}−z_{t,high}∥² plus a constant. Minimizing that negative log-density is therefore the same sum as Rhigh by construction. The proof only re-derives this identity and calls it a "Bayesian justification"; no likelihood, posterior, or additional data constraint is supplied. Any quadratic temporal-difference penalty is MAP under some Gaussian random-walk prior, so the lemma adds no independent theoretical ground beyond the already-defined loss term.

  2. other [Section 3.3, Theorem 1; Appendix B.4, Eq. (37) and Assumption 2, Eq. (15); Sec. 3.1 defines the unseen target.]
    "Assumption 2 ... Rn(G) on any sequence of n samples drawn from a target domain DT+1 ... bounded as: Rn(G)≤ C/√n. ... More directly, the generalization gap for our specific predictor ˆθT+1 (derived from z∈Rm) is: EPT+1[ℓ(g(X; ˆθT+1),Y)]≤ En[ℓ(g(X; ˆθT+1),Y)] + 2LℓLg C/√n + LℓLg √(B² log(1/δ)/2n)."

    Section 3.1 defines TDG as generalizing to a future target domain DT+1 "without access to DT+1 during training." The proof of Theorem 1 bounds the true target risk by the empirical risk En over "the draw of n samples for DT+1." In the actual TDG setting no such n exists, so the O(1/√n) estimation term is vacuous: it assumes the very target samples whose absence defines the problem. The first term is also not an external check, since Elow and Ehigh are unquantified errors of FreKoo's own latent predictors, and Lemma 1 only bounds their propagation under ρ(K)<1 without any training constraint enforcing that condition. The theorem therefore restates target risk in terms of target-sample risk plus slack rather than deriving generalization from the spectral-Koopman mechanism.

full rationale

The empirical contribution of FreKoo is evaluated against seven external benchmarks with a standard protocol, and those results are not circular: the reported gains on 2-Moons, Elec2, Appliance, and the other datasets stand independently of the paper's theoretical framing. The derivation chain, however, contains two self-referential moves. First, Lemma 2 presents the high-frequency temporal-difference penalty as a principled Bayesian justification, but the Gaussian random-walk prior is chosen so that its MAP objective is exactly the already-defined Rhigh; the Appendix proof is a restatement of this equivalence, not an independent ground. Second, Theorem 1's multiscale generalization bound relies on an empirical Rademacher complexity and an empirical risk term defined on n samples drawn from the unseen target domain D_{T+1}; because the TDG setting explicitly excludes access to D_{T+1} during training, the O(1/√n) term is vacuous and the theorem does not establish a bound connecting FreKoo's spectral-Koopman mechanism to target generalization. These issues make the 'rigorous theoretical foundation' claim partly circular or vacuous, though they do not invalidate the empirical evaluation. No load-bearing self-citation chain was found; the paper's self-citations are not used to justify the central derivation.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the spectral-separation premise and on a learned Koopman linearization. Hyperparameters tau, alpha, beta, gamma are tuned per dataset, adding flexibility but also making the 'robust' claim dataset-conditioned rather than parameter-free.

free parameters (5)
  • Energy preservation ratio tau = 0.9 (2-Moons, Rot-MNIST, Shuttle), 0.8 (ONP, Appliance), 0.1 (Elec2), 0.3 (House)
    Controls how many dominant frequency bins are treated as low-frequency signal; tuned per dataset in Appendix C.3.
  • Loss weight alpha = 10 (2-Moons, Elec2), 0.1 (Rot-MNIST, ONP, House), 1 (Shuttle, Appliance)
    Balances the parameter reconstruction loss L_rec; tuned per dataset.
  • Loss weight beta = 1 (2-Moons, Rot-MNIST, ONP, Shuttle, Appliance), 0.1 (Elec2), 10 (House)
    Balances the Koopman dynamics loss L_koop; tuned per dataset.
  • Loss weight gamma = 1 (2-Moons, Rot-MNIST, Shuttle, Elec2, House), 0.01 (ONP), 100 (Appliance)
    Balances the high-frequency smoothing regularizer R_high; tuned per dataset.
  • Koopman latent dimension m = 32 (all datasets)
    Hand-set architecture choice for the encoder/decoder latent space.
assumptions (6)
  • domain assumption Parameter evolution follows theta_{t+1} = Phi(theta_t) + epsilon_t with deterministic Phi and stochastic epsilon_t (Eq. 1).
    Frames TDG as parameter trajectory prediction; asserted in Section 3.2 without empirical validation.
  • domain assumption Dominant drift patterns (incremental and periodic) are concentrated in low-frequency components of the parameter trajectory; transient uncertainties are high-frequency.
    Core inductive bias of FreKoo; used to justify the spectral mask in Eq. (4)-(5) and the whole low/high split.
  • domain assumption The low-frequency parameter trajectory is well approximated by a finite-dimensional linear Koopman operator K in a learned latent space.
    Assumed in Eq. (6)-(7); the Koopman representation for nonlinear dynamics is approximate and requires a sufficiently rich observable space.
  • standard math Encoders and decoder are L-Lipschitz (Assumption 1).
    Used in Theorem 1's proof; plausible for MLPs but not verified in the paper.
  • standard math The induced hypothesis class has Rademacher complexity C/sqrt(n) and target samples are beta-mixing (Assumption 2).
    Standard learning-theoretic assumption; the beta-mixing property is not used beyond invoking the complexity bound.
  • domain assumption The target-domain optimal parameter theta*_{T+1} lies in the hypothesis class reachable by the decoder.
    Implicit in Theorem 1's proof when comparing to theta*; if theta* is outside the class, the excess-risk decomposition does not hold.

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Cite this review

Pith. "Pith review of Learning Robust Spectral Dynamics for Temporal Domain Generalization." pith.science (2026). https://pith.science/paper/PXYN4DCT

@misc{pith2026250512585,
  author       = {Pith},
  title        = {Pith review of: Learning Robust Spectral Dynamics for Temporal Domain Generalization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PXYN4DCT}},
  note         = {Machine review of arXiv:2505.12585}
}
read the original abstract

Modern machine learning models struggle to maintain performance in dynamic environments where temporal distribution shifts, \emph{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.

Figures

Figures reproduced from arXiv: 2505.12585 by the authors.

Figure 1
Figure 1. Illustration of challenges in TDG. Left: Complex drifting situations can involve both [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FreKoo Framework. It decomposes model parameter trajectories into low-frequency and high-frequency components via the Fourier transform. Then, Koopman operator is employed to learn the evolution of low-frequency dynamics, enabling robust prediction of incremental trend and periodicity. Also, it introduces a targeted tempo￾ral difference regularization to the high-frequency components, promoting smooth convergence an… view at source ↗
Figure 4
Figure 4. Parameters sensitivity on 2-Moons and Appliance datasets. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Periodicity modeling performance on P-Moons dataset. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 5
Figure 5. Figure 5: Visualization of domain-specific uncertainties on real-world datasets. [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: Visualization of decision boundaries on the 2-Moons dataset. Blue dots and red stars [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: Visualization of parameter evolution for different components on the P-2-Moons dataset. [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]

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Works this paper leans on

48 extracted references · 40 canonical work pages

  1. [1]

    Huang, K

    Han, E., C. Huang, K. Wang. Model assessment and selection under temporal distribution shift. In R. Salakhutdinov, Z. Kolter, K. Heller, A. Weller, N. Oliver, J. Scarlett, F. Berkenkamp, eds., Proceedings of the 41st International Conference on Machine Learning, vol. 235 of Proceedings of Machine Learning Research, pages 17374–17392. PMLR, 2024

    work page 2024

  2. [2]

    Wang, R., Y . Dong, S. Arik, et al. Koopman neural forecaster for time series with temporal distribution shifts. In International Conference on Learning Representations (ICLR). 2023

    work page 2023

  3. [3]

    Lu, J., A. Liu, F. Dong, et al. Learning under concept drift: A review. IEEE transactions on knowledge and data engineering, 31(12):2346–2363, 2018

    work page 2018

  4. [4]

    Xu, K., L. Chen, S. Wang. Coral: Concept drift representation learning for co-evolving time-series. arXiv preprint arXiv:2501.01480, 2025

    arXiv 2025

  5. [5]

    Wang, J., Z. Ren, R. Zhan, et al. Distributionally robust policy learning under concept drifts. arXiv preprint arXiv:2412.14297, 2024

    work page Pith review arXiv 2024

  6. [6]

    Thakur, V

    Nasery, A., S. Thakur, V . Piratla, et al. Training for the future: A simple gradient interpolation loss to generalize along time. Advances in Neural Information Processing Systems, 34:19198– 19209, 2021

    work page 2021

  7. [7]

    Chuang, Z

    Chang, C.-Y ., Y .-N. Chuang, Z. Jiang, et al. Coda: Temporal domain generalization via concept drift simulator. arXiv preprint arXiv:2310.01508, 2023

    arXiv 2023

  8. [8]

    Bai, G., C. Ling, L. Zhao. Temporal domain generalization with drift-aware dynamic neural networks. In The Eleventh International Conference on Learning Representations. 2023

    work page 2023

Show all 48 references
  1. [9]

    Jin, Y ., Z. Yang, X. Chu, et al. Temporal domain generalization via learning instance-level evolving patterns. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, pages 4255–4263. 2024

    2024

  2. [10]

    Zeng, Q., W. Wang, F. Zhou, et al. Foresee what you will learn: data augmentation for domain generalization in non-stationary environment. In Proceedings of the AAAI conference on artificial intelligence, vol. 37, pages 11147–11155. 2023

    2023

  3. [11]

    Generalizing across temporal domains with koopman operators

    —. Generalizing across temporal domains with koopman operators. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38, pages 16651–16659. 2024

    2024

  4. [12]

    Cai, Z., G. Bai, R. Jiang, et al. Continuous temporal domain generalization. arXiv preprint arXiv:2405.16075, 2024

    2024 arXiv

  5. [13]

    Yu, E., J. Lu, B. Zhang, et al. Online boosting adaptive learning under concept drift for multistream classification. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38, pages 16522–16530. 2024

    2024

  6. [14]

    Jiao, B., Y . Guo, D. Gong, et al. Dynamic ensemble selection for imbalanced data streams with concept drift. IEEE Transactions on Neural Networks and Learning Systems, 2022

    2022

  7. [15]

    Niu, S., J. Wu, Y . Zhang, et al. Towards stable test-time adaptation in dynamic wild world. In The Eleventh International Conference on Learning Representations. 2023. 10

    2023

  8. [16]

    Liu, Y ., C. Li, J. Wang, et al. Koopa: Learning non-stationary time series dynamics with koopman predictors. Advances in neural information processing systems, 36:12271–12290, 2023

    2023

  9. [17]

    Cheng, Z

    Liu, Z., M. Cheng, Z. Li, et al. Adaptive normalization for non-stationary time series forecasting: A temporal slice perspective. In Thirty-seventh Conference on Neural Information Processing Systems. 2024

    2024

  10. [18]

    Ye, H., J. Chen, S. Gong, et al. Atfnet: Adaptive time-frequency ensembled network for long-term time series forecasting. arXiv preprint arXiv:2404.05192, 2024

    2024 arXiv

  11. [19]

    Ye, W., S. Deng, Q. Zou, et al. Frequency adaptive normalization for non-stationary time series forecasting. In The Thirty-eighth Annual Conference on Neural Information Processing Systems. 2024

    2024

  12. [20]

    Koopman, B. O. Hamiltonian systems and transformation in hilbert space. Proceedings of the National Academy of Sciences, 17(5):315–318, 1931

    1931

  13. [21]

    Brunton, S. L., M. Budiši´c, E. Kaiser, et al. Modern koopman theory for dynamical systems. arXiv preprint arXiv:2102.12086, 2021

    2021 arXiv

  14. [22]

    Wang, H., H. He, D. Katabi. Continuously indexed domain adaptation. In Proceedings of the 37th International Conference on Machine Learning, pages 9898–9907. 2020

    2020

  15. [23]

    Lu, P., J. Lu, A. Liu, et al. Early concept drift detection via prediction uncertainty. InProceedings of the AAAI Conference on Artificial Intelligence, vol. 39, pages 19124–19132. 2025

    2025

  16. [24]

    Jiao, B., Y . Guo, S. Yang, et al. Reduced-space multistream classification based on multiobjective evolutionary optimization. IEEE Transactions on Evolutionary Computation, 27(4):764–777, 2023

    2023

  17. [25]

    Yang, X., J. Lu, E. Yu. Adapting multi-modal large language model to concept drift from pre-training onwards. In The Thirteenth International Conference on Learning Representations. 2025

    2025

  18. [26]

    Zhou, T., Z. Ma, Q. Wen, et al. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In International conference on machine learning , pages 27268–27286. PMLR, 2022

    2022

  19. [27]

    Yi, K., J. Fei, Q. Zhang, et al. Filternet: Harnessing frequency filters for time series forecasting. Advances in Neural Information Processing Systems, 37:55115–55140, 2024

    2024

  20. [28]

    Cutler, R., L. S. Davis. Robust real-time periodic motion detection, analysis, and applications. IEEE Transactions on pattern analysis and machine intelligence, 22(8):781–796, 2000

    2000

  21. [29]

    Zhang, A

    Hurley-Walker, N., X. Zhang, A. Bahramian, et al. A radio transient with unusually slow periodic emission. Nature, 601(7894):526–530, 2022

    2022

  22. [30]

    Wang, B., M. Tian, Y . Yu, et al. Enhanced adrc with quasi-resonant control for pmsm speed reg- ulation considering aperiodic and periodic disturbances. IEEE Transactions on Transportation Electrification, 8(3):3568–3577, 2021

    2021

  23. [31]

    Smékal, J., J. T. Smith, M. Kleinman, et al. Towards a theory of learning dynamics in deep state space models. arXiv preprint arXiv:2407.07279, 2024

    2024 arXiv

  24. [32]

    Qin, D., Y . Li, W. Chen, et al. Evolving multi-scale normalization for time series forecasting under distribution shifts. arXiv preprint arXiv:2409.19718, 2024

    2024 arXiv

  25. [33]

    Ortiz-Jimenez, G., M. E. Gheche, E. Simou, et al. Cdot: Continuous domain adaptation using optimal transport. arXiv preprint arXiv:1909.11448, 2019

    1909 arXiv

  26. [34]

    Qin, T., S. Wang, H. Li. Generalizing to evolving domains with latent structure-aware sequential autoencoder. In International Conference on Machine Learning, pages 18062–18082. PMLR, 2022. 11

    2022

  27. [35]

    Xie, M., S. Li, L. Yuan, et al. Evolving standardization for continual domain generalization over temporal drift. Advances in Neural Information Processing Systems, 36, 2024

    2024

  28. [36]

    Li, J., Z. Yu, Z. Du, et al. A comprehensive survey on source-free domain adaptation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024

    2024

  29. [37]

    Yu, E., J. Lu, G. Zhang. Fuzzy shared representation learning for multistream classification. IEEE Transactions on Fuzzy Systems, 32(10):5625–5637, 2024

    2024

  30. [38]

    Liu, M., X. Chen, Y . Shu, et al. Boosting transferability and discriminability for time series domain adaptation. Advances in Neural Information Processing Systems, 37:100402–100427, 2024

    2024

  31. [39]

    Khoee, A. G., Y . Yu, R. Feldt. Domain generalization through meta-learning: A survey.Artificial Intelligence Review, 57(10):285, 2024

    2024

  32. [40]

    Wang, R., H. Zuo, Z. Fang, et al. Towards robustness prompt tuning with fully test-time adaptation for clip’s zero-shot generalization. In ACM Multimedia 2024. 2024

    2024

  33. [41]

    Peng, K., D. Wen, K. Yang, et al. Advancing open-set domain generalization using evidential bi- level hardest domain scheduler. Advances in Neural Information Processing Systems, 37:85412– 85440, 2024

    2024

  34. [42]

    Chakrabarty, M

    Nayak, I., A. Chakrabarty, M. Kumar, et al. Temporally-consistent koopman autoencoders for forecasting dynamical systems. arXiv preprint arXiv:2403.12335, 2024

    2024 arXiv

  35. [43]

    LI, Z., M. Han, X. Yin. MamKO: Mamba-based koopman operator for modeling and predictive control. In The Thirteenth International Conference on Learning Representations. 2025

    2025

  36. [44]

    Machine learning foundations

    Jo, T. Machine learning foundations. Supervised, Unsupervised, and Advanced Learning. Cham: Springer International Publishing, 6(3):8–44, 2021

    2021

  37. [45]

    Arora, S., S. Du, W. Hu, et al. Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. In International conference on machine learning, pages 322–332. PMLR, 2019

    2019

  38. [46]

    Horn, R. A., C. R. Johnson. Matrix analysis. Cambridge university press, 2012. 12 Appendix A Additional Related Works Domain Adaptation/Generalization. Domain Adaptation (DA) requires access to both source and target domain data during training, employing methods like domain-i...

    2012

  39. [47]

    (30) Equivalence toRhigh: The regularization term isRhigh =PT−1 t=1 ∥zt+1,high−zt,high∥2

  40. [48]

    Raw Parameter

    Minimiz- ingRhigh is equivalent to minimizing 1 2σ2Rhigh, since 1 2σ2 is a positive constant. This shows that minimizingRhigh is equivalent to MAP estimation under the specified Gaussian random-walk prior with precisionλprior = 1/(2σ2). This encourages smoothness in the trajec...

    2019

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.