Pith. sign in

REVIEW 2 major objections 2 minor 60 references

VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read VLBM separates stable ID dynamics from OOD deviations in multivariate time series by decomposing inputs into a shared latent basis subspace and orthogonal residuals.

desk verdict VLBM combines variational inference, low-rank basis decomposition, and orthogonal residuals to target OOD robustness in time series, but the abstract supplies no verification that the decomposition actually separates stable dynamics from shifts. read the letter →

arxiv 2606.02138 v1 pith:STP6HP2G submitted 2026-06-01 cs.LG cs.AI

Xudong Zhang , Jierui Lei , Jiacheng Li , Lingdong Shen , Jian Cui , Haina Tang This is my paper · ORCID
classification cs.LGcs.AI
keywords multivariatetimeseriesforecastingout-of-distributionrobustnessvariationallatentmodelsbasisdecompositiondistributionshiftrobustprediction
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

The paper sets out to show that standard training on mixed ID and OOD time series lets frequent normal patterns drown out rare but high-impact shifts, so average accuracy does not guarantee reliability when OOD events matter most. VLBM counters this by learning one shared latent basis that spans the stable low-rank subspace of ID behavior, splitting every input into basis components plus orthogonal residuals, and forcing a future-aware posterior to match a future-blind prior. The result is that inference at test time uses only past observations and the model isolates deviations without retraining. If the separation holds, forecasts can stay accurate even when OOD pulses dominate real-world risk across transportation, weather, and power data.

What carries the argument

shared latent basis that defines a low-rank subspace for stable ID dynamics together with explicit decomposition into basis and residual components and alignment of future-aware posterior to future-blind prior

What would settle it

If VLBM shows no MAE or MSE improvement over the strongest baseline on the twelve benchmarks, especially the new real-world OOD traffic datasets, the performance and separation claims would be falsified.

Watch

Extended reading notes

Core claim

VLBM learns a shared latent basis that defines a low-rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future-aware posterior with a future-blind prior so that test-time latent inference depends only on historical input, producing state-of-the-art OOD robustness and ID accuracy on twelve real-world tasks with average MAE and MSE gains of 15.08 percent and 7.74 percent over the strongest baseline.

Load-bearing premise

Decomposing inputs into a shared latent basis for stable patterns plus orthogonal residuals, while aligning a future-aware posterior to a future-blind prior, will keep ID patterns from overwhelming training and will make test-time inference depend only on historical data.

Editorial extensions

If this is right

  • Optimization no longer lets frequent ID patterns drown rare OOD signals during training.
  • Test-time forecasts remain reliable under high-impact distribution shifts without needing explicit OOD labels.
  • Latent structured forecasting supplies a route to robust prediction when ID and OOD data are mixed.
  • Better tracking of OOD pulses appears on synthetic simulations that isolate deviation recovery.

Reading between the lines

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

  • The same basis-plus-residual split could be tested on other sequential domains where rare events drive risk, such as financial or sensor streams.
  • The orthogonal decomposition supplies an implicit way to interpret which parts of a series count as stable versus deviant.
  • Replacing the future-blind prior with other variational constraints might extend the robustness gain beyond time series.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper proposes VLBM, a variational latent basis model for multivariate time series forecasting that learns a shared low-rank latent basis to capture stable ID dynamics, explicitly decomposes inputs into basis-subspace and orthogonal-residual components, and aligns a future-aware posterior with a future-blind prior so that test-time inference uses only historical inputs. It reports state-of-the-art OOD robustness and ID accuracy across 12 real-world benchmarks (transportation, weather, power, plus newly constructed OOD traffic datasets) with average MAE/MSE gains of 15.08%/7.74% over the strongest baseline, plus superior performance on a synthetic OOD-pulse dataset.

Significance. If the claimed separation between stable ID dynamics and OOD deviations is mechanistically validated, the framework would address a practically important gap between average-case accuracy and reliability under high-impact shifts. Public code release is a clear strength supporting reproducibility.

major comments (2)
  1. [Abstract / §3] Abstract and §3 (method): the central robustness claim—that the orthogonal residual isolates OOD-induced deviations while the shared basis captures only stable ID dynamics, with the posterior/prior alignment guaranteeing history-only test-time inference—receives no supporting derivation, component-norm analysis, or ablation showing that residual norms are reliably larger on OOD samples than on ID samples. Without this evidence the reported 15% MAE gain cannot be attributed to the stated mechanism rather than other modeling choices.
  2. [§4] §4 (experiments): the headline average gains of 15.08% MAE / 7.74% MSE are presented without per-dataset breakdowns, statistical significance tests, or ablation tables that isolate the contribution of the orthogonal-residual term versus the latent-basis term. This makes it impossible to verify whether the OOD robustness result holds consistently or is driven by a subset of tasks.
minor comments (2)
  1. [§3] Notation for the latent basis rank and variational hyperparameters should be introduced with explicit symbols and ranges in §3 rather than left implicit.
  2. [§4] The synthetic simulation experiment would benefit from a figure showing recovered OOD pulse trajectories alongside ground truth to illustrate the claimed tracking improvement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the robustness claims and experimental reporting. We will revise the manuscript to strengthen the mechanistic evidence and provide the requested granular results.

read point-by-point responses

  1. Referee: [Abstract / §3] Abstract and §3 (method): the central robustness claim—that the orthogonal residual isolates OOD-induced deviations while the shared basis captures only stable ID dynamics, with the posterior/prior alignment guaranteeing history-only test-time inference—receives no supporting derivation, component-norm analysis, or ablation showing that residual norms are reliably larger on OOD samples than on ID samples. Without this evidence the reported 15% MAE gain cannot be attributed to the stated mechanism rather than other modeling choices.

    Authors: We agree that the current presentation would benefit from an explicit derivation and supporting analysis. In the revised §3 we will add a formal derivation of the orthogonality between the basis subspace and residual under the variational alignment objective, along with the proof that the future-blind prior enables history-only inference at test time. We will also add a component-norm analysis subsection in the experiments that reports average residual norms on ID versus OOD samples across the 12 benchmarks to show that OOD deviations concentrate in the residual. These additions will directly address attribution of the reported gains. revision: yes

  2. Referee: [§4] §4 (experiments): the headline average gains of 15.08% MAE / 7.74% MSE are presented without per-dataset breakdowns, statistical significance tests, or ablation tables that isolate the contribution of the orthogonal-residual term versus the latent-basis term. This makes it impossible to verify whether the OOD robustness result holds consistently or is driven by a subset of tasks.

    Authors: We acknowledge that the headline averages alone are insufficient for verification. In the revision we will expand §4 with complete per-dataset tables (including means and standard deviations over multiple runs), paired statistical significance tests (Wilcoxon signed-rank) against the strongest baseline on each task, and dedicated ablation tables that isolate the orthogonal-residual term and the latent-basis term by removing each component in turn. These tables will demonstrate consistency across the transportation, weather, power, and synthetic OOD-pulse settings. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity detected; new modeling framework with empirical results

full rationale

The provided abstract and text introduce VLBM as a novel variational latent basis model that explicitly constructs a shared low-rank basis, decomposes inputs into subspace and orthogonal residual components, and aligns a future-aware posterior with a future-blind prior. No equations, derivations, or mathematical reductions are visible that would make any claimed prediction or result equivalent to its inputs by construction. Performance claims rest on reported benchmark experiments across 12 tasks and synthetic data rather than algebraic identities, fitted parameters renamed as predictions, or self-citation chains. The framework is presented as an independent proposal rather than a re-expression of prior fitted results, making the derivation self-contained against external benchmarks.

Assumptions & free parameters 2 free parameters · 2 assumptions · 2 invented entities

The approach rests on several modeling assumptions about the existence of a stable low-rank subspace and the utility of variational alignment; these are introduced to enable the claimed separation but lack independent verification in the abstract.

free parameters (2)
  • latent basis rank
    The dimension of the shared low-rank subspace is a modeling choice that must be selected or tuned and directly affects the decomposition into basis and residual components.
  • variational hyperparameters
    Parameters controlling the posterior-prior alignment and reconstruction loss weights are fitted or chosen to achieve the reported performance.
assumptions (2)
  • domain assumption Multivariate time series inputs admit a decomposition into a low-rank shared basis subspace capturing stable ID dynamics and an orthogonal residual capturing OOD deviations.
    This decomposition is the central structural assumption that allows the model to isolate OOD effects.
  • domain assumption Aligning a future-aware posterior with a future-blind prior ensures that test-time inference uses only historical input.
    This alignment is invoked to guarantee that the model does not leak future information at deployment.
invented entities (2)
  • Shared latent basis
    purpose: Defines the low-rank subspace for stable ID dynamics.
    New modeling construct introduced to separate stable from deviating components.
  • Orthogonal residual component
    purpose: Captures OOD-induced deviations outside the basis subspace.
    New component postulated to isolate rare events.

how reviews work

0 comments
Cite this review

Pith. "Pith review of VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting." pith.science (2026). https://pith.science/paper/STP6HP2G

@misc{pith2026260602138,
  author       = {Pith},
  title        = {Pith review of: VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/STP6HP2G}},
  note         = {Machine review of arXiv:2606.02138}
}
read the original abstract

Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08\% and 7.74\% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.

Figures

Figures reproduced from arXiv: 2606.02138 by the authors.

Figure 1
Figure 1. Conceptual overview of OOD robust forecasting under mixed ID/OOD conditions. (a) Observed time series are partial projections of latent system [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Overall architecture of VLBM. (a) Input embedding maps raw [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Controlled simulation on the Synthetic Graph Pulse benchmark. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Forecasting comparison under ID and OOD conditions. (a) Forecasting results on the CHP-LCS-Speed dataset, evaluated on anomalous intervals [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Visualization of learned latent basis. (a) UMAP visualization of latent [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Visualization of pathway representations. (a) Base path representation [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Ablation study on CHP-LCS-Flow (OOD) and ECL (ID) in averaged [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 3 canonical work pages

  1. [1]

    A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection,

    M. Jinet al., “A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection,”IEEE Trans. Pattern Anal. Mach. Intell., 2024

    2024

  2. [2]

    Self-supervised learning for time series analysis: Taxonomy, progress, and prospects,

    K. Zhanget al., “Self-supervised learning for time series analysis: Taxonomy, progress, and prospects,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 46, no. 10, pp. 6775–6794, 2024

    2024

  3. [3]

    Timedart: A diffusion au- toregressive transformer for self-supervised time series representation,

    D. Wang, M. Cheng, Z. Liu, and Q. Liu, “Timedart: A diffusion au- toregressive transformer for self-supervised time series representation,” arXiv:2410.05711, 2024

    work page arXiv 2024

  4. [4]

    Transformer- plm enhanced multimodal time series forecasting via decoupled dual- temporal graph adaptation,

    J. Lei, W. Zhang, Q. Yang, X. Zhang, and H. Tang, “Transformer- plm enhanced multimodal time series forecasting via decoupled dual- temporal graph adaptation,”IEEE Signal Process. Lett., vol. 33, pp. 11–15, 2025

    2025

  5. [5]

    The republic,

    C. Plato, “The republic,” inDemocracy: A Reader. Columbia University Press, 2016, pp. 229–233

    2016

  6. [6]

    Diversify: A general framework for time series out-of- distribution detection and generalization,

    W. Luet al., “Diversify: A general framework for time series out-of- distribution detection and generalization,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 46, no. 6, pp. 4534–4550, 2024

    2024

  7. [7]

    Stpdn: Spatio-temporal pattern decomposition network with fluctuation aware- ness for robust traffic flow forecasting,

    X. Zhang, P. Peng, X. Chen, Y . Wu, L. Shen, and H. Tang, “Stpdn: Spatio-temporal pattern decomposition network with fluctuation aware- ness for robust traffic flow forecasting,” inECAI 2024, 2024, pp. 2588– 2596

    2024

  8. [8]

    Time-series forecasting for out-of-distribution generalization using in- variant learning,

    H. Liu, H. Kamarthi, L. Kong, Z. Zhao, C. Zhang, and B. A. Prakash, “Time-series forecasting for out-of-distribution generalization using in- variant learning,”arXiv:2406.09130, 2024

    work page arXiv 2024

Show all 60 references
  1. [9]

    A time series is worth 64words: Long-term forecasting with transformers,

    Y . Nie, “A time series is worth 64words: Long-term forecasting with transformers,” inProc. Int. Conf. Learn. Representations, 2023

    2023

  2. [10]

    itransformer: Inverted transformers are effective for time series forecasting,

    Y . Liuet al., “itransformer: Inverted transformers are effective for time series forecasting,” inProc. Int. Conf. Learn. Representations, 2024

    2024

  3. [11]

    Moderntcn: A modern pure convolution structure for general time series analysis,

    D. Luo and X. Wang, “Moderntcn: A modern pure convolution structure for general time series analysis,” inProc. Int. Conf. Learn. Representa- tions, 2024

    2024

  4. [12]

    Sundial: A family of highly capable time series foundation models,

    Y . Liuet al., “Sundial: A family of highly capable time series foundation models,” inProc. 42nd Int. Conf. Mach. Learn., 2025

    2025

  5. [13]

    Patch-wise structural loss for time series forecasting,

    D. Kudrat, Z. Xie, Y . Sun, T. Jia, and Q. Hu, “Patch-wise structural loss for time series forecasting,”arXiv:2503.00877, 2025

    2025

  6. [14]

    Graph wavenet for deep spatial-temporal graph modeling,

    Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep spatial-temporal graph modeling,” inProc. 28th Int. Joint Conf. Artif. Intell., 2019

    2019

  7. [15]

    Adaptive graph convolutional recurrent network for traffic forecasting,

    L. Bai, L. Yao, C. Li, X. Wang, and C. Wang, “Adaptive graph convolutional recurrent network for traffic forecasting,” inProc. Adv. Neural Inf. Process. Syst., vol. 33, 2020, pp. 17 804–17 815

    2020

  8. [16]

    Adpstgcn: Adaptive spatial–temporal graph convolu- tional network for traffic forecasting,

    X. Zhanget al., “Adpstgcn: Adaptive spatial–temporal graph convolu- tional network for traffic forecasting,”Knowl.-Based Syst., vol. 301, p. 112295, 2024

    2024

  9. [17]

    Graph convolutional adversarial networks for spatiotemporal anomaly detection,

    L. Deng, D. Lian, Z. Huang, and E. Chen, “Graph convolutional adversarial networks for spatiotemporal anomaly detection,”IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 6, pp. 2416–2428, 2022

    2022

  10. [18]

    Timestacker: A novel framework with multilevel observation for capturing nonstationary patterns in time series forecasting,

    Q. Liu, C. Xu, W. Jiang, K. Wang, L. Ma, and H. Li, “Timestacker: A novel framework with multilevel observation for capturing nonstationary patterns in time series forecasting,” inProc. 42nd Int. Conf. Mach. Learn., 2025

    2025

  11. [19]

    When will it fail?: Anomaly to prompt for forecasting future anomalies in time series,

    M.-Y . Park, W.-J. Lee, S. T. Kim, and G.-M. Park, “When will it fail?: Anomaly to prompt for forecasting future anomalies in time series,” in Proc. 42nd Int. Conf. Mach. Learn., 2025

    2025

  12. [20]

    Spatial-temporal identity: A simple yet effective baseline for multivariate time series forecasting,

    Z. Shao, Z. Zhang, F. Wang, W. Wei, and Y . Xu, “Spatial-temporal identity: A simple yet effective baseline for multivariate time series forecasting,” inProc. 31st ACM Int. Conf. Inf. Knowl. Manag., 2022, pp. 4454–4458

    2022

  13. [21]

    Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,

    H. Wu, J. Xu, J. Wang, and M. Long, “Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,” in Proc. Adv. Neural Inf. Process. Syst., vol. 34, 2021, pp. 22 419–22 430

    2021

  14. [22]

    Are transformers effective for time series forecasting?

    A. Zeng, M. Chen, L. Zhang, and Q. Xu, “Are transformers effective for time series forecasting?” inProc. AAAI Conf. Artif. Intell., vol. 37, no. 9, 2023, pp. 11 121–11 128

    2023

  15. [23]

    A memory guided transformer for time series forecasting,

    Y . Cheng, C. Guo, B. Yang, H. Yu, K. Zhao, and C. S. Jensen, “A memory guided transformer for time series forecasting,”Proc. VLDB Endow., vol. 18, no. 2, pp. 239–252, 2024

    2024

  16. [24]

    Dualcast: A model to disentangle aperiodic events from traffic series,

    X. Su, F. Liu, Y . Chang, E. Tanin, M. Sarvi, and J. Qi, “Dualcast: A model to disentangle aperiodic events from traffic series,” inProc. 34th Int. Joint Conf. Artif. Intell., 2025, pp. 3290–3298

    2025

  17. [25]

    Time series representations with hard-coded invariances,

    T. Germain, C. Kosma, and L. Oudre, “Time series representations with hard-coded invariances,” inProc. 42nd Int. Conf. Mach. Learn., 2025

    2025

  18. [26]

    Freeformer: Fre- quency enhanced transformer for multivariate time series forecasting,

    W. Yue, Y . Liu, X. Ying, B. Xing, R. Guo, and J. Shi, “Freeformer: Fre- quency enhanced transformer for multivariate time series forecasting,” inProc. 34th Int. Joint Conf. Artif. Intell., 2025, pp. 3606–3614

    2025

  19. [27]

    Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting,

    Y . Zhang and J. Yan, “Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting,” inProc. 11th Int. Conf. Learn. Representations, 2023

    2023

  20. [28]

    Dgraformer: Dynamic graph learning guided multi-scale transformer for multivariate time series forecasting,

    H. Yanet al., “Dgraformer: Dynamic graph learning guided multi-scale transformer for multivariate time series forecasting,” inProc. 34th Int. Joint Conf. Artif. Intell., 2025, pp. 3516–3524

    2025

  21. [29]

    Time-LLM: Time series forecasting by reprogramming large language models,

    M. Jinet al., “Time-LLM: Time series forecasting by reprogramming large language models,” inProc. Int. Conf. Learn. Representations, 2024

    2024

  22. [30]

    Timecma: Towards llm-empowered multivariate time series forecasting via cross-modality alignment,

    C. Liuet al., “Timecma: Towards llm-empowered multivariate time series forecasting via cross-modality alignment,” inProc. AAAI Conf. Artif. Intell., vol. 39, no. 18, 2025, pp. 18 780–18 788

    2025

  23. [31]

    Unified training of universal time series forecasting transformers,

    G. Woo, C. Liu, A. Kumar, C. Xiong, S. Savarese, and D. Sahoo, “Unified training of universal time series forecasting transformers,” in Proc. 41st Int. Conf. Mach. Learn., 2024

    2024

  24. [32]

    Time-moe: Billion-scale time series foundation models with mixture of experts,

    X. Shiet al., “Time-moe: Billion-scale time series foundation models with mixture of experts,” inProc. Int. Conf. Learn. Representations, 2025

    2025

  25. [33]

    Towards a general time series forecasting model with unified representation and adaptive transfer,

    Y . Wanget al., “Towards a general time series forecasting model with unified representation and adaptive transfer,” inProc. 42nd Int. Conf. Mach. Learn., vol. 267, 2025, pp. 64 127–64 151

    2025

  26. [34]

    Timemixer: Decomposable multiscale mixing for time series forecasting,

    S. Wanget al., “Timemixer: Decomposable multiscale mixing for time series forecasting,” inProc. Int. Conf. Learn. Representations, 2024

    2024

  27. [35]

    TimeBase: The power of minimalism in efficient long-term time series forecasting,

    Q. Huang, Z. Zhou, K. Yang, Z. Yi, X. Wang, and Y . Wang, “TimeBase: The power of minimalism in efficient long-term time series forecasting,” inProc. 42nd Int. Conf. Mach. Learn., vol. 267, 2025, pp. 26 227– 26 246

    2025

  28. [36]

    Temporal query network for efficient multivariate time series forecasting,

    S. Lin, H. Chen, H. Wu, C. Qiu, and W. Lin, “Temporal query network for efficient multivariate time series forecasting,” inProc. 42nd Int. Conf. Mach. Learn., vol. 267, 2025, pp. 37 797–37 814

    2025

  29. [37]

    Timesnet: Temporal 2d-variation modeling for general time series analysis,

    H. Wu, T. Hu, Y . Liu, H. Zhou, J. Wang, and M. Long, “Timesnet: Temporal 2d-variation modeling for general time series analysis,” in Proc. 11th Int. Conf. Learn. Representations, 2023

    2023

  30. [38]

    Msgnet: Learning multi- scale inter-series correlations for multivariate time series forecasting,

    W. Cai, Y . Liang, X. Liu, J. Feng, and Y . Wu, “Msgnet: Learning multi- scale inter-series correlations for multivariate time series forecasting,” in Proc. AAAI Conf. Artif. Intell., vol. 38, no. 10, 2024, pp. 11 141–11 149

    2024

  31. [39]

    TimeFilter: Patch-specific spatial-temporal graph filtration for time series forecasting,

    Y . Huet al., “TimeFilter: Patch-specific spatial-temporal graph filtration for time series forecasting,” inProc. 42nd Int. Conf. Mach. Learn., vol. 267, 2025, pp. 24 893–24 911

    2025

  32. [40]

    Agga-mvfln: Multivariate time series forecasting via adaptive generalized graph accompanied with multi-view learning in frequency domain,

    J. Lei, F. Chen, and H. Tang, “Agga-mvfln: Multivariate time series forecasting via adaptive generalized graph accompanied with multi-view learning in frequency domain,” inProc. ACM Int. Conf. Multimedia Retrieval, 2025, pp. 653–661

    2025

  33. [41]

    Collaborative multivariate time series forecasting via variable-tailored inter-temporal graph and adaptive- smooth frequency fusion,

    J. Lei, P. Peng, H. Tanget al., “Collaborative multivariate time series forecasting via variable-tailored inter-temporal graph and adaptive- smooth frequency fusion,”Mach. Learn., vol. 115, no. 3, p. 49, 2026

    2026

  34. [42]

    Timekan: Kan-based frequency decomposition learning architecture for long-term time series forecast- ing,

    S. Huang, Z. Zhao, C. Li, and L. BAI, “Timekan: Kan-based frequency decomposition learning architecture for long-term time series forecast- ing,” inProc. Int. Conf. Learn. Representations, 2025

    2025

  35. [43]

    TimePro: Efficient multivariate long-term time series forecasting with variable- and time-aware hyper- state,

    X. Ma, Z.-L. Ni, S. Xiao, and X. Chen, “TimePro: Efficient multivariate long-term time series forecasting with variable- and time-aware hyper- state,” inProc. 42nd Int. Conf. Mach. Learn., vol. 267, 2025, pp. 42 096– 42 111

    2025

  36. [44]

    The capacity and robustness trade- off: Revisiting the channel independent strategy for multivariate time series forecasting,

    L. Han, H.-J. Ye, and D.-C. Zhan, “The capacity and robustness trade- off: Revisiting the channel independent strategy for multivariate time series forecasting,”IEEE Trans. Knowl. Data Eng., vol. 36, no. 11, pp. 7129–7142, 2024

    2024

  37. [45]

    Stone: A spatio-temporal ood learning framework kills both spatial and temporal shifts,

    B. Wanget al., “Stone: A spatio-temporal ood learning framework kills both spatial and temporal shifts,” inProc. 30th ACM SIGKDD Conf. Knowl. Discov. Data Mining, 2024, pp. 2948–2959. 13

    2024

  38. [46]

    Decoupled dynamic spatial-temporal graph neural network for traffic forecasting,

    Z. Shaoet al., “Decoupled dynamic spatial-temporal graph neural network for traffic forecasting,”Proc. VLDB Endow., vol. 15, no. 11, pp. 2733–2746, 2022

    2022

  39. [47]

    Bist: A lightweight and efficient bi-directional model for spatiotemporal prediction,

    J. Ma, B. Wang, P. Wang, Z. Zhou, X. Wang, and Y . Wang, “Bist: A lightweight and efficient bi-directional model for spatiotemporal prediction,”Proc. VLDB Endow., vol. 18, no. 6, pp. 1663–1676, 2025

    2025

  40. [48]

    Seeing the unseen: Learning basis confounder representations for robust traffic prediction,

    J. Ji, W. Zhang, J. Wang, and C. Huang, “Seeing the unseen: Learning basis confounder representations for robust traffic prediction,” inProc. 31st ACM SIGKDD Conf. Knowl. Discov. Data Mining V .1, 2025, pp. 577–588

    2025

  41. [49]

    Catch: Channel-aware multivariate time series anomaly detection via frequency patching,

    X. Wuet al., “Catch: Channel-aware multivariate time series anomaly detection via frequency patching,” inProc. 13th Int. Conf. Learn. Representations, 2025

    2025

  42. [50]

    Tab: Unified benchmarking of time series anomaly detection methods,

    X. Qiuet al., “Tab: Unified benchmarking of time series anomaly detection methods,”Proc. VLDB Endow., vol. 18, no. 9, pp. 2775–2789, 2025

    2025

  43. [51]

    Towards a general time series anomaly detector with adaptive bottlenecks and dual adversarial decoders,

    Q. Shentuet al., “Towards a general time series anomaly detector with adaptive bottlenecks and dual adversarial decoders,” inProc. Int. Conf. Learn. Representations, 2025

    2025

  44. [52]

    Pinkus,N-widths in Approximation Theory

    A. Pinkus,N-widths in Approximation Theory. Springer, 2012

    2012

  45. [53]

    Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality,

    F. Otto and C. Villani, “Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality,”J. Funct. Anal., vol. 173, no. 2, pp. 361–400, 2000

    2000

  46. [54]

    Villaniet al.,Optimal transport: old and new

    C. Villaniet al.,Optimal transport: old and new. Springer, 2009, vol. 338

    2009

  47. [55]

    Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding,

    K. Hundman, V . Constantinou, C. Laporte, I. Colwell, and T. Soder- strom, “Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding,” inProc. 24th ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2018, pp. 387–395

    2018

  48. [56]

    Practical approach to asyn- chronous multivariate time series anomaly detection and localization,

    A. Abdulaal, Z. Liu, and T. Lancewicki, “Practical approach to asyn- chronous multivariate time series anomaly detection and localization,” inProc. 27th ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2021, pp. 2485–2494

    2021

  49. [57]

    Duet: Dual clustering enhanced multivari- ate time series forecasting,

    X. Qiu, X. Wu, Y . Linet al., “Duet: Dual clustering enhanced multivari- ate time series forecasting,” inProc. 31st ACM SIGKDD Conf. Knowl. Discov. Data Mining, 2025, pp. 1185–1196

    2025

  50. [58]

    Timemixer++: A general time series pattern machine for universal predictive analysis,

    S. Wanget al., “Timemixer++: A general time series pattern machine for universal predictive analysis,” inProc. Int. Conf. Learn. Representations, 2025

    2025

  51. [59]

    Filterts: Comprehensive frequency filtering for multivariate time series forecasting,

    Y . Wang, Y . Liu, X. Duan, and K. Wang, “Filterts: Comprehensive frequency filtering for multivariate time series forecasting,” inProc. AAAI Conf. Artif. Intell., vol. 39, no. 20, 2025, pp. 21 375–21 383

    2025

  52. [60]

    Spatio-temporal meta-graph learning for traffic fore- casting,

    R. Jianget al., “Spatio-temporal meta-graph learning for traffic fore- casting,” inProc. AAAI Conf. Artif. Intell., vol. 37, no. 7, 2023, pp. 8078–8086

    2023

Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.