Pith. sign in

REVIEW 5 major objections 5 minor 47 references

Multivariate Long-term Time Series Forecasting with Fourier Neural Filter

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read A Fourier-based backbone with parallel temporal and spatial branches reports the best mean absolute error on all 11 multivariate long-term forecasting benchmarks, without auxiliary decomposition modules.

desk verdict A plausible new architecture with consistent MAE wins across 11 datasets, but the SOTA claim is not yet established: margins are within noise, no variance is reported, and the lookback protocol is asymmetric. read the letter →

arxiv 2506.09174 v2 pith:XNNHB5VN submitted 2025-06-10 cs.LG

Chenheng Xu , Dan Wu , Yixin Zhu , Ying Nian Wu This is my paper
classification cs.LG
keywords multivariatetimeseriesforecastinglong-termFourierneuraloperatorfrequency-domainfilteringdual-brancharchitectureinformationbottleneckpatchembeddingmeanabsoluteerror
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 argues that long-term multivariate forecasting has been held back by reusing backbones from language and vision, which do not naturally handle periodicity and local-global structure. To fix this it proposes the Fourier Neural Filter (FNF), an input-dependent Fourier kernel that acts as a gated global convolution and combines local time-domain and global frequency-domain information in one operation at $O(N\log N)$ cost. It wraps FNF in a Dual Branch Design (DBD) that processes temporal patterns and cross-variable spatial patterns in parallel, rather than unifying or chaining them, with information-bottleneck reasoning for why parallel processing preserves information and gradient flow. On 11 datasets spanning energy, weather, traffic, air quality, and plant-flow measurements, FNF+DBD reports the best average MAE on every dataset and best or near-best MSE across four forecast horizons, with consistent hyperparameters and no decomposition modules. The paper's conclusion is that a time-series-specific backbone can carry the modeling load that current methods push onto auxiliary techniques.

What carries the argument

The load-bearing object is the Fourier Neural Filter (FNF), an integral kernel operator whose kernel $\kappa(x,y;v)$ depends on the input. In implementation it is a gated global convolution: a linear expansion produces a local GELU-gated branch, while a Fourier transform, complex linear layers with softshrink denoising, and an inverse Fourier transform produce a global frequency-filtered branch, and their element-wise (Hadamard) product is projected by a linear map. The surrounding architecture, DBD, runs two FNF stacks in parallel, one over time and one over variables, and fuses them with a sigmoid-gated weighted sum. The filter gives $O(N\log N)$ token mixing without a separate feed-forward network, and the theoretical analysis shows that parallel branches preserve more task-relevant mutual information and offer shorter gradient paths than unified or sequential alternatives.

What would settle it

Run the Table 2 comparison symmetrically: evaluate every baseline at lookback 512 as well as at its best lookback, evaluate FNF at lookback 96 as well as 512, average MAE over at least five seeds, and check whether FNF still has the best MAE on all 11 datasets.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that a forecasting architecture can reach state-of-the-art multivariate long-term accuracy without auxiliary signal decomposition if the backbone is designed for time series. FNF generalizes the Fourier Neural Operator by making the integration kernel $\kappa(x,y;v)$ depend on the input, so the filter adapts to each input's local magnitude and phase rather than staying fixed. The element-wise product of a GELU-gated local branch and a Fourier-domain filtered branch implements selective activation, suppressing, preserving, or amplifying frequency components at each position. DBD then runs two FNF filters in parallel, one temporal and one spatial, and fuses them with an input-dependent gate; the paper derives an information-bottleneck inequality to argue that parallel processing keeps more mutual information about the target and offers shorter gradient paths than unified or sequential designs. The empirical claim is that this combination attains the lowest MAE on all 11 benchmarks, with larger percentage gains in MAE than in MSE, under a single consistent hyperparameter setting.

Load-bearing premise

The headline result rests on the assumption that a fixed 512-step history for FNF is a fair comparison against baselines at their best-tuned histories, and that the reported MAE margins would survive seed-to-seed variation.

Editorial extensions

If this is right

  • On the paper's 11 benchmarks, FNF+DBD reports the lowest average MAE on every dataset, with stronger percentage gains in MAE than in MSE.
  • Because the model errs less on the majority of timesteps, it is better suited to long-horizon operational forecasting than to settings where isolated extreme errors dominate.
  • The $O(N\log N)$ token-mixing complexity and the absence of a separate feed-forward network make the backbone cheaper than quadratic-attention Transformers at long lookbacks.
  • The information-bottleneck analysis predicts that unified and sequential spatio-temporal designs are structurally lossy, so future multivariate architectures should keep temporal and spatial pathways parallel.
  • If the central claim holds, auxiliary signal decomposition is unnecessary when the backbone itself supplies periodicity-aware local and global processing.

Reading between the lines

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

  • Editorial inference: the same information-bottleneck reasoning should extend to other multivariate sequence tasks, such as imputation, classification, and anomaly detection, which the paper's Limitations section lists as untested.
  • Editorial inference: the reported margins depend on an asymmetric lookback choice; the paper's own sensitivity table shows FNF's air-quality errors rise when lookback drops from 512 to 96, so a symmetric protocol could narrow or invert the lead.
  • Editorial inference: the paper's MAE-over-MSE pattern implies a testable per-horizon win-rate claim, namely that FNF should beat the best baseline on most individual forecast horizons, not only on averages.
  • Editorial inference: because FNF internalizes both token mixing and feed-forward expansion, it could serve as a drop-in mixer inside other sequence-processing architectures that currently rely on attention.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes Fourier Neural Filter (FNF), a backbone built on Fourier Neural Operators with an input-dependent kernel, and a Dual Branch Design (DBD) that processes temporal and spatial information in parallel branches. The authors claim FNF unifies local time-domain and global frequency-domain processing, that DBD provides superior gradient flow and representation capacity from an information-bottleneck perspective, and that FNF+DBD achieves state-of-the-art multivariate long-term forecasting on 11 benchmark datasets with consistent hyperparameter settings and no auxiliary techniques. The empirical section reports average MSE/MAE over horizons 96/192/336/720 across 11 datasets, with ablations on the backbone (Transformer/FNO/FNF), architecture (independent/unified/sequential/parallel), and lookback sensitivity.

Significance. If the empirical claim holds, FNF+DBD would be a useful, efficient backbone for long-term forecasting: it reports O(N log N) complexity, avoids decomposition-based auxiliary modules, and the ablations isolate the contribution of the FNF backbone and the parallel design. The use of external public benchmarks and eight published baselines gives the empirical comparison independent grounding. However, the state-of-the-art claim is currently not established: the evaluation protocol is asymmetric (FNF uses lookback 512 while baselines are tuned over {96, 336, 512}), the margins over the closest baselines are small, no variance or significance information is reported, and no code is released. The theoretical sections are largely restatements of the architecture rather than proofs, so the paper's central contribution rests on the empirical evaluation, which needs strengthening.

major comments (5)
  1. [Section 5, Settings; Table 2; Table 5] The evaluation protocol is asymmetric. Baselines are evaluated at their optimal lookback among {96, 336, 512} per the TFB protocol, while FNF is fixed at lookback 512. Table 5 shows that on AQShunyi the average MAE at lookback 96 is 0.509 versus 0.491 at 512, so the fixed lookback materially contributes to the reported gains. The margins in Table 2 are small (e.g., Weather MAE 0.255 vs. 0.257, AQWan 0.479 vs. 0.482, ETTh1 0.417 vs. 0.421), and a symmetric protocol—either evaluating all baselines at lookback 512 or tuning FNF over the same lookback set—could shrink or reverse the claimed improvements. Please report results under a symmetric protocol or provide a convincing justification for the fixed lookback.
  2. [Section 5, Settings; Appendix D; Abstract] The abstract and Section 5 claim 'consistent hyperparameter settings' with a fixed embedding dimension of 128, but Appendix D states that the embedding dimension is increased to 256 for Electricity, Weather, and Traffic and reduced to 64 for AQShunyi and AQWan. Table A3, which is the fine-tuned set, is what supports the headline numbers in Table 2 for those datasets. This directly contradicts the consistency claim, and the manuscript needs to either remove the 'consistent hyperparameter settings' claim or clearly report which results use the default and which use the per-dataset fine-tuned settings.
  3. [Appendix B.2; Section 3.1.2] The derivation of the 'gated global convolution' does not establish that FNF computes a convolution. In Eq. (A13), the term G(v)(x) multiplies the convolution output at position x, and the constructed kernel in Eq. (A14) depends on the output coordinate x, not on the difference x-y. The text itself acknowledges 'This formulation does not directly constitute a convolution' and then defines an alternative kernel ~tildeκ_v(x-y) that absorbs G(v)(x). This is a relabeling of the Hadamard-product architecture, not a proof that FNF unifies local time-domain and global frequency-domain processing. Please reframe Section 3.1 and Appendix B.2 as architectural motivation rather than a proof, or provide a genuine functional derivation.
  4. [Section 3.2, Eq. (17)] The claim that the parallel architecture has superior representation capacity relies on the inequality I(T1,T2;Y) > max{I(T1;Y), I(T2;Y)}, which is justified by asserting that temporal and spatial features are 'fundamentally orthogonal.' This is an assumption about learned representations, not a consequence of the information-bottleneck formalism, and it is not empirically verified. As written, the information-bottleneck 'demonstration' is circular with respect to the parallel design. Please either provide evidence (e.g., mutual-information estimates on the trained branches) or explicitly label this as a heuristic motivation.
  5. [Section 5, Results; all tables] No per-seed variance, error bars, or statistical significance tests are reported. Given that several headline margins are within 1% in MAE (Weather 0.255 vs. 0.257, AQWan 0.479 vs. 0.482, ETTh1 0.417 vs. 0.421), the state-of-the-art assertion is not distinguishable from seed-to-seed variability. Please report mean and standard deviation over at least three (preferably five) seeds for FNF and the nearest baselines, and consider a paired significance test across the common test windows.
minor comments (5)
  1. [Section 3.1, Eq. (4)] The Hadamard product is denoted by 'd', which is nonstandard and easy to confuse with a differential; the paper should use ⊙ throughout, as in Section 3.1.3.
  2. [Figure 2 caption; Section 3.1.4; Appendix B.3] The caption says 'two complex linear layers' but Appendix B.3 describes 'four linear layers' in the frequency branch; please reconcile the count and describe the exact operations.
  3. [Table A1] The Weather dataset description says 'Recorded every for the whole year 2020' and is missing a time unit; it should state 'every 10 minutes' as in Table 1.
  4. [Section 2, Distribution Shift] The phrase 'Liet al. [25]' is informal; please give the full citation in the text at first mention.
  5. [Throughout] The text contains many typographical artifacts, such as 'OpNlogNq', 'D 2', and 'pŸvqpxq' in inline math; these should be cleaned up before publication.

Circularity Check

1 steps flagged · score 4.0 of 10

Empirical SOTA comparisons are grounded in external benchmarks, but the paper's theoretical claim that FNF 'unifies' local time-domain and global frequency-domain information is a restatement of the architecture's defining Hadamard product, not a derived result.

  1. self definitional [Abstract; Section 3.1.3, Definition 5 and Remark 3 (Eqs. 4 and 7)]
    "The selective activation mechanism in FNF operates through Hadamard product between local information G(v)(x) and global information P(v)(x)... Remark 3: This formulation reveals how selective activation simultaneously modulates both amplitude (through multiplication |G(v)_i|·|P(v)_i|) and phase (through addition θ_G(v)_i + θ_P(v)_i)."

    FNF is defined in Eq. (4) as T(G(v)(x) ⊙ F^{-1}(R_phi · F(H(v))))(x), where the G branch is labeled 'local time-domain' and the Fourier branch is labeled 'global frequency-domain'. The paper's claim that FNF 'unifies' these two kinds of information is then 'proved' by defining selective activation as the Hadamard product of the two branches (Eq. 7) and remarking that the product multiplies magnitudes and adds phases. That is an unpacking of the definition, not a consequence derived from an independent principle or theorem. The theoretical novelty claim therefore reduces, by construction, to the design choice made when writing Eq. (4).

full rationale

The headline state-of-the-art claim is not circular: Table 2 reports errors measured against eight external baselines on 11 public datasets, and those numbers do not follow algebraically from the model definition. I found no load-bearing self-citation, no fitted parameter renamed as a prediction, and no imported uniqueness theorem. The genuine circularity is confined to the theoretical framing: the assertion that FNF 'unifies' local and global information is true by definition of the Hadamard-product architecture, and the DBD section's information-bottleneck inequalities likewise assert, rather than prove, that parallel branches are superior to sequential ones. The empirical evaluation also has a fairness/robustness concern (FNF fixed at lookback 512 while baselines use TFB-optimal lookbacks, and no error bars are reported), but that is not circularity. Because the central empirical claims have independent support and only the supporting theory reduces to a restatement of the construction, a score of 4 is appropriate.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The architecture's design choices, especially the per-dataset embedding dimension and the FNF lookback of 512, are free parameters that influence the reported margins. The main theoretical premises are the unproven orthogonality of temporal/spatial features (Eq. 17) and the assumption that the FNF implementation can be treated as an exact input-dependent integral kernel despite nonlinearities. No new physical entities are introduced; the input-dependent kernel is the paper's central invented construct, and its only falsifiable handle so far is the in-paper benchmark evaluation.

free parameters (3)
  • embedding_dimension = 128 default; 256 for Electricity, Weather, Traffic; 64 for AQShunyi, AQWan in fine-tuned results
    Hand-tuned per dataset in Appendix D (Table A3) to improve results. The main tables use 128 everywhere, but the fine-tuned runs show the model is sensitive to this knob.
  • softshrink_threshold_lambda = not reported
    Appears in Eq. 9 as the frequency-domain denoising threshold; its value is never given, so the reader cannot replicate the spectral filtering exactly. Chosen by hand, unstated.
  • lookback_window = 512 for FNF; 96/336/512 grid for baselines
    The paper fixes FNF at 512 while baselines are allowed their optimal lookback. The paper's own Table 5 shows a 9% MSE swing between lookback 96 and 512 on AQ datasets, so this choice is material to the claimed margin.
assumptions (4)
  • standard math Data-processing inequality for the sequential chain X -> T1 -> T2 -> Y (Eq. 12)
    Correct application of the data-processing inequality; not a weakness.
  • ad hoc to paper Temporal and spatial features are sufficiently orthogonal that I(T1,T2;Y) > max{I(T1;Y), I(T2;Y)} (Eq. 17)
    Unproven; the paper asserts complementarity without computing or bounding any mutual information for the actual architecture. This is load-bearing for the DBD superiority claim.
  • domain assumption The FNF operator can be represented as an integral kernel with input-dependent kappa(x,y;v) under the implementation in Eq. 4 (Appendix B.1)
    The derivation assumes H(v)=W_h v is a linear transformation and that T can be pulled through the Hadamard product and integral. Acceptable for the abstract operator, but the paper's own implementation also includes nonlinear activations (GELU, Softshrink) and BatchNorm, which break strict linearity of the 'kernel'.
  • domain assumption Information bottleneck (Tishby-Zaslavsky) is a valid criterion for comparing neural architectures' representation capacity (Section 3.2)
    The theory is used qualitatively; the paper does not compute IB Lagrangians or show that the proposed branches optimize the stated objectives (Eq. 14).
invented entities (1)
  • Input-dependent gated global convolution kernel kappa(x,y;v)
    purpose: Claims to unify local time-domain and global frequency-domain processing in one operator
    Introduced in Definition 2 and Remark 1. No falsifiable prediction outside the benchmark suite; it is an architectural description rather than an independently testable entity. The empirical benchmarks are internal to the paper's evaluation, not external predictions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Multivariate Long-term Time Series Forecasting with Fourier Neural Filter." pith.science (2026). https://pith.science/paper/XNNHB5VN

@misc{pith2026250609174,
  author       = {Pith},
  title        = {Pith review of: Multivariate Long-term Time Series Forecasting with Fourier Neural Filter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XNNHB5VN}},
  note         = {Machine review of arXiv:2506.09174}
}
read the original abstract

Multivariate long-term time series forecasting has been suffering from the challenge of capturing both temporal dependencies within variables and spatial correlations across variables simultaneously. Current approaches predominantly repurpose backbones from natural language processing or computer vision (e.g., Transformers), which fail to adequately address the unique properties of time series (e.g., periodicity). The research community lacks a dedicated backbone with temporal-specific inductive biases, instead relying on domain-agnostic backbones supplemented with auxiliary techniques (e.g., signal decomposition). We introduce FNF as the backbone and DBD as the architecture to provide excellent learning capabilities and optimal learning pathways for spatio-temporal modeling, respectively. Our theoretical analysis proves that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling, while information bottleneck theory demonstrates that DBD provides superior gradient flow and representation capacity compared to existing unified or sequential architectures. Our empirical evaluation across 11 public benchmark datasets spanning five domains (energy, meteorology, transportation, environment, and nature) confirms state-of-the-art performance with consistent hyperparameter settings. Notably, our approach achieves these results without any auxiliary techniques, suggesting that properly designed neural architectures can capture the inherent properties of time series, potentially transforming time series modeling in scientific and industrial applications.

Figures

Figures reproduced from arXiv: 2506.09174 by the authors.

Figure 1
Figure 1. Radar chart of forecasting performance across 11 benchmark datasets spanning five do￾mains. The chart displays average MAE across differ￾ent forecast horizons of 96, 192, 336, 720. Our pro￾posed FNF (highlighted) consistently outperforms eight strong baseline models on diverse domains of energy, weather, transportation, environment, and nature with consistent hyperparameter settings. Time series forecasting, which p… view at source ↗
Figure 2
Figure 2. The FNF backbone. Our dual￾branch design processes input embeddings through parallel expanded linear layers [45]. The right branch captures time-domain pat￾terns via GELU activation [38], while the left branch extracts frequency-domain fea￾tures through Fourier transform, complex operations [17] (two complex linear lay￾ers with Softshrink function [39]), and in￾verse Fourier transform. The branches are combined via … view at source ↗
Figure 3
Figure 3. The Dual Branch Design (DBD) architecture. Each approach pro￾cesses multivariate time series in shape pB, M, L, Dq differently: (a) Unified: single backbone simultaneously models temporal and spatial patterns; (b) Sequen￾tial: cascades temporal filter followed by spatial filter; (c) Parallel: applies indepen￾dent temporal and spatial filters in sepa￾rate branches. Our DBD implements the parallel design to effectivel… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Schematic diagram of our proposed neural architecture. Where, normalization for mitigating distribution shift, embedding for obtaining informative input embeddings, backbone for addressing temporal dependencies and spatial correlations, and projection for generating pr…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

47 extracted references · 45 canonical work pages

  1. [1]

    Tfb: Towards comprehensive and fair benchmarking of time series forecasting methods

    Xiangfei Qiu, Jilin Hu, Lekui Zhou, Xingjian Wu, Junyang Du, Buang Zhang, Chenjuan Guo, Aoying Zhou, Christian S Jensen, Zhenli Sheng, and others. Tfb: Towards comprehensive and fair benchmarking of time series forecasting methods. InProceedings of International Conference on Very Large Data Bases (VLDB), 2024. 1, 7

    work page 2024

  2. [2]

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

    Shiyu Wang, Jiawei Li, Xiaoming Shi, Zhou Ye, Baichuan Mo, Wenze Lin, Shengtong Ju, Zhixuan Chu, and Ming Jin. Timemixer++: A general time series pattern machine for universal predictive analysis. InProceedings of International Conference on Learning Representations (ICLR), 2025. 1, 2

    work page 2025

  3. [3]

    A machine learning model for hub-height short-term wind speed prediction.Nature Communi- cations, 16(1):3195, 2025

    Zongwei Zhang, Lianlei Lin, Sheng Gao, Junkai Wang, Hanqing Zhao, and Hangyi Yu. A machine learning model for hub-height short-term wind speed prediction.Nature Communi- cations, 16(1):3195, 2025. 1

    work page 2025

  4. [4]

    Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators

    Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopad- hyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, and others. Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators. InProceedings of International Conference on Learning Representati...

    work page 2022

  5. [5]

    Accurate medium-range global weather forecasting with 3d neural networks.Nature, 619(7970):533– 538, 2023

    Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian. Accurate medium-range global weather forecasting with 3d neural networks.Nature, 619(7970):533– 538, 2023. 1

    work page 2023

  6. [6]

    Informer: Beyond efficient transformer for long sequence time-series forecasting

    Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2021. 1, 3, 7, A1

    work page 2021

  7. [7]

    Forecasting at scale.The American Statistician, 72(1):37–45, 2018

    Sean J Taylor and Benjamin Letham. Forecasting at scale.The American Statistician, 72(1):37–45, 2018. 2

    work page 2018

  8. [8]

    N-beats: Neural ba- sis expansion analysis for interpretable time series forecasting

    Boris N Oreshkin, Dmitri Carpov, Nicolas Chapados, and Yoshua Bengio. N-beats: Neural ba- sis expansion analysis for interpretable time series forecasting. InProceedings of International Conference on Learning Representations (ICLR), 2020. 2

    work page 2020

Show all 47 references
  1. [9]

    Peri- odicity decoupling framework for long-term series forecasting

    Tao Dai, Beiliang Wu, Peiyuan Liu, Naiqi Li, Jigang Bao, Yong Jiang, and Shu-Tao Xia. Peri- odicity decoupling framework for long-term series forecasting. InProceedings of International Conference on Learning Representations (ICLR), 2024. 2

    2024

  2. [10]

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

    Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. InProceedings of International Conference on Learning Representations (ICLR), 2022. 2, 3, 6, 7

    2022

  3. [11]

    Multi- resolution time-series transformer for long-term forecasting

    Yitian Zhang, Liheng Ma, Soumyasundar Pal, Yingxue Zhang, and Mark Coates. Multi- resolution time-series transformer for long-term forecasting. InInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2024. 2, 3

    2024

  4. [12]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. InProceedings of Advances in Neural Information Processing Systems (NeurIPS), 2017. 2 10

    2017

  5. [13]

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

    Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. InProceedings of Interna- tional Conference on Learning Representations (ICLR), 2022. 2, 3, 7

    2022

  6. [14]

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

    Donghao Luo and Xue Wang. Moderntcn: A modern pure convolution structure for general time series analysis. InProceedings of International Conference on Learning Representations (ICLR), 2024. 2, 3

    2024

  7. [15]

    Are transformers effective for time series forecasting? InProceedings of AAAI Conference on Artificial Intelligence (AAAI), 2023

    Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? InProceedings of AAAI Conference on Artificial Intelligence (AAAI), 2023. 2, 7

    2023

  8. [16]

    Fourier neural operator for parametric partial dif- ferential equations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial dif- ferential equations. InProceedings of International Conference on Learning Representations (ICLR), 2...

    2021

  9. [17]

    Adaptive fourier neural operators: Efficient token mixers for transformers

    John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, and Bryan Catanzaro. Adaptive fourier neural operators: Efficient token mixers for transformers. In Proceedings of International Conference on Learning Representations (ICLR), 2022. 2, 3, 4

    2022

  10. [18]

    Crossformer: Transformer utilizing cross-dimension depen- dency for multivariate time series forecasting

    Yunhao Zhang and Junchi Yan. Crossformer: Transformer utilizing cross-dimension depen- dency for multivariate time series forecasting. InProceedings of International Conference on Learning Representations (ICLR), 2023. 2, 3, 5, 7

    2023

  11. [19]

    From similarity to superiority: Channel clustering for time series forecasting

    Jialin Chen, Jan Eric Lenssen, Aosong Feng, Weihua Hu, Matthias Fey, Leandros Tassiulas, Jure Leskovec, and Rex Ying. From similarity to superiority: Channel clustering for time series forecasting. InProceedings of Advances in Neural Information Processing Systems (NeurIPS),

  12. [20]

    Deep learning and the information bottleneck principle

    Naftali Tishby and Noga Zaslavsky. Deep learning and the information bottleneck principle. InIEEE Information Theory Workshop (ITW), 2015. 2, 5

    2015

  13. [21]

    Pathformer: Multi-scale transformers with adaptive pathways for time series forecasting

    Peng Chen, Yingying Zhang, Yunyao Cheng, Yang Shu, Yihang Wang, Qingsong Wen, Bin Yang, and Chenjuan Guo. Pathformer: Multi-scale transformers with adaptive pathways for time series forecasting. InProceedings of International Conference on Learning Representa- tions (ICLR), 20...

    2024

  14. [22]

    Deep adaptive input normalization for time series forecasting.IEEE Transactions on Neural Networks and Learning Systems, 31(9):3760–3765, 2019

    Nikolaos Passalis, Anastasios Tefas, Juho Kanniainen, Moncef Gabbouj, and Alexandros Iosi- fidis. Deep adaptive input normalization for time series forecasting.IEEE Transactions on Neural Networks and Learning Systems, 31(9):3760–3765, 2019. 2

    2019

  15. [23]

    Ddn: Dual-domain dynamic normalization for non-stationary time series forecasting

    Tao Dai, Beiliang Wu, Peiyuan Liu, Naiqi Li, Xue Yuerong, Shu-Tao Xia, and Zexuan Zhu. Ddn: Dual-domain dynamic normalization for non-stationary time series forecasting. InPro- ceedings of Advances in Neural Information Processing Systems (NeurIPS), 2024. 2

    2024

  16. [24]

    Time- bridge: Non-stationarity matters for long-term time series forecasting

    Peiyuan Liu, Beiliang Wu, Yifan Hu, Naiqi Li, Tao Dai, Jigang Bao, and Shu-tao Xia. Time- bridge: Non-stationarity matters for long-term time series forecasting. InProceedings of Inter- national Conference on Machine Learning (ICML), 2025. 2

    2025

  17. [25]

    Revisiting long-term time series forecasting: An investigation on linear mapping.arXiv preprint arXiv:2305.10721, 2023

    Zhe Li, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting long-term time series forecasting: An investigation on linear mapping.arXiv preprint arXiv:2305.10721, 2023. 2

    2023 arXiv

  18. [26]

    Reversible instance normalization for accurate time-series forecasting against distribution shift

    Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. Reversible instance normalization for accurate time-series forecasting against distribution shift. InProceedings of International Conference on Learning Representations (ICLR), 2021. 2, 6

    2021

  19. [27]

    Dish-ts: A general paradigm for alleviating distribution shift in time series forecasting

    Wei Fan, Pengyang Wang, Dongkun Wang, Dongjie Wang, Yuanchun Zhou, and Yanjie Fu. Dish-ts: A general paradigm for alleviating distribution shift in time series forecasting. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2023. 2

    2023

  20. [28]

    Adaptive normalization for non-stationary time series forecasting: A temporal slice perspec- tive

    Zhiding Liu, Mingyue Cheng, Zhi Li, Zhenya Huang, Qi Liu, Yanhu Xie, and Enhong Chen. Adaptive normalization for non-stationary time series forecasting: A temporal slice perspec- tive. InProceedings of Advances in Neural Information Processing Systems (NeurIPS), 2023. 2 11

    2023

  21. [29]

    Frequency adaptive normalization for non-stationary time series forecasting

    Weiwei Ye, Songgaojun Deng, Qiaosha Zou, and Ning Gui. Frequency adaptive normalization for non-stationary time series forecasting. InProceedings of Advances in Neural Information Processing Systems (NeurIPS), 2024. 2

    2024

  22. [30]

    Prformer: Pyramidal recurrent trans- former for multivariate time series forecasting

    Yongbo Yu, Weizhong Yu, Feiping Nie, and Xuelong Li. Prformer: Pyramidal recurrent trans- former for multivariate time series forecasting. InProceedings of AAAI Conference on Artifi- cial Intelligence (AAAI), 2024. 2, 3

    2024

  23. [31]

    Learning to embed time series patches inde- pendently

    Seunghan Lee, Taeyoung Park, and Kibok Lee. Learning to embed time series patches inde- pendently. InProceedings of International Conference on Learning Representations (ICLR),

  24. [32]

    Hdmixer: Hierarchical dependency with extendable patch for multivariate time series forecasting

    Qihe Huang, Lei Shen, Ruixin Zhang, Jiahuan Cheng, Shouhong Ding, Zhengyang Zhou, and Yang Wang. Hdmixer: Hierarchical dependency with extendable patch for multivariate time series forecasting. InProceedings of AAAI Conference on Artificial Intelligence (AAAI), 2024. 3

    2024

  25. [33]

    Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting

    Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting. InProceedings of Advances in Neural Information Processing Systems (NeurIPS), 2021. 3, 7, A1

    2021

  26. [34]

    A decoder-only foundation model for time-series forecasting

    Abhimanyu Das, Weihao Kong, Rajat Sen, and Yichen Zhou. A decoder-only foundation model for time-series forecasting. InProceedings of International Conference on Machine Learning (ICML), 2024. 3

    2024

  27. [35]

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

    Xiaoming Shi, Shiyu Wang, Yuqi Nie, Dianqi Li, Zhou Ye, Qingsong Wen, and Ming Jin. Time-moe: Billion-scale time series foundation models with mixture of experts. InProceedings of International Conference on Learning Representations (ICLR), 2025. 3

    2025

  28. [36]

    Fredf: Learning to forecast in frequency domain

    Hao Wang, Licheng Pan, Zhichao Chen, Degui Yang, Sen Zhang, Yifei Yang, Xinggao Liu, Haoxuan Li, and Dacheng Tao. Fredf: Learning to forecast in frequency domain. InProceed- ings of International Conference on Learning Representations (ICLR), 2024. 3

    2024

  29. [37]

    Rectified linear units improve restricted boltzmann ma- chines

    Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann ma- chines. InProceedings of International Conference on Machine Learning (ICML), 2010. 4

    2010

  30. [38]

    Gaussian error linear units (gelus).arXiv preprint arXiv:1606.08415, 2016

    Dan Hendrycks and Kevin Gimpel. Gaussian error linear units (gelus).arXiv preprint arXiv:1606.08415, 2016. 3, 4

    2016 arXiv

  31. [39]

    De-noising by soft-thresholding.IEEE Transactions on Information Theory, 41(3):613–627, 2002

    David L Donoho. De-noising by soft-thresholding.IEEE Transactions on Information Theory, 41(3):613–627, 2002. 3, 4

    2002

  32. [40]

    Deep variational infor- mation bottleneck

    Alexander A Alemi, Ian Fischer, Joshua V Dillon, and Kevin Murphy. Deep variational infor- mation bottleneck. InProceedings of International Conference on Learning Representations (ICLR), 2017. 5

    2017

  33. [41]

    Non-local neural networks

    Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. InProceedings of Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 5

    2018

  34. [42]

    Learning representations by back-propagating errors.Nature, 323(6088):533–536, 1986

    David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. Learning representations by back-propagating errors.Nature, 323(6088):533–536, 1986. 7

    1986

  35. [43]

    itransformer: Inverted transformers are effective for time series forecasting

    Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer: Inverted transformers are effective for time series forecasting. InProceed- ings of International Conference on Learning Representations (ICLR), 2023. 3, 7

    2023

  36. [44]

    Zhang, and Jun Zhou

    Shiyu Wang, Haixu Wu, Xiao Long Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y . Zhang, and Jun Zhou. Timemixer: Decomposable multiscale mixing for time series forecasting. In Proceedings of International Conference on Learning Representations (ICLR), 2024. 7

    2024

  37. [45]

    Mamba: Linear-time sequence modeling with selective state spaces

    Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces. InProceedings of International Conference on Language Modeling, 2024. 3 12

    2024

  38. [46]

    Cautionary tales on air-quality improvement in beijing.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2205):20170457, 2017

    Shuyi Zhang, Bin Guo, Anlan Dong, Jing He, Ziping Xu, and Song Xi Chen. Cautionary tales on air-quality improvement in beijing.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2205):20170457, 2017. 7, A1

    2017

  39. [47]

    Global transpiration data from sap flow measurements: the SAPFLUXNET database.Earth System Science Data Discussions, 2020:1–57, 2020

    Rafael Poyatos, Víctor Granda, Víctor Flo, Mark A Adams, Balázs Adorján, David Aguadé, Marcos PM Aidar, Scott Allen, M Susana Alvarado-Barrientos, Kristina J Anderson-Teixeira, and others. Global transpiration data from sap flow measurements: the SAPFLUXNET database.Earth Syst...

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.