Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting

Dung Nguyen; Hung Le; Huu Hiep Nguyen; Minh Hoang Nguyen

REVIEW 3 major objections 6 minor 2 cited by

Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting

T0 review · 3 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper claims that modulating the time-series spectrum with text-derived complex vectors—via cross-attention and multiplication in the frequency domain—yields more accurate forecasts than time-domain multimodal fusion.

desk verdict SpecTF is a genuinely new frequency-domain cross-attention fusion for text + time series, but the 'significant' gains are not backed by error bars and the text-as-frequency framing is an assumption. read the letter →

arxiv 2602.01588 v3 pith:HUNLCKHK submitted 2026-02-02 cs.LG cs.AI

Huu Hiep Nguyen , Minh Hoang Nguyen , Dung Nguyen , Hung Le This is my paper

classification cs.LGcs.AI MSC 68T0762M1068T50

keywords multimodaltime-seriesforecastingfrequency-domainfusionspectraltextcross-modalattentiontext-enhancedFouriertransformcomplex-valuedneuralnetworksprediction

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 proposes SpecTF, a forecasting framework that incorporates textual context by operating on the spectral components of the time series rather than through step-by-step temporal alignment. It argues that text influences multiple temporal scales at once—short-term fluctuations and long-term trends—and that frequency-domain fusion captures this multiscale effect naturally. The central result is that SpecTF outperforms strong unimodal and multimodal baselines on eight of nine domains in the Time-MMD benchmark and on two additional climate and medical datasets, while using markedly fewer parameters. The key idea is that text can reweight and phase-shift individual frequency bands of the historical series before the spectrum is inverted back to the time domain for prediction.

What carries the argument

FreqCMF (Frequency Cross-Modality Fusion) is the central mechanism. It consists of (1) frequency cross-attention, where time-series spectral queries attend to text-derived complex keys and values, producing an attention-weighted text vector for each frequency band; and (2) multiplication fusion, an elementwise complex multiplication of the spectrum and the text vector. The paper invokes the convolution theorem to argue that this multiplication corresponds to a global convolution in the time domain, and Parseval's theorem to argue that energy is preserved.

What would settle it

If the textual 'frequency' embeddings are replaced by random complex vectors (or by the same embeddings permuted across frequency bands) and forecast error does not change, then the frequency structure attributed to text is not actually being exploited. More directly, one can test the convolution claim by feeding a time series with a single impulse through the fusion and checking whether the output equals the convolution of that impulse with any fixed kernel derived from the text embedding.

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Extended reading notes

Core claim

The paper's central claim is that text-to-time-series fusion is best performed in the frequency domain. After applying the real FFT to the input series, a lightweight cross-attention mechanism lets each frequency band query the textual embeddings, and a complex multiplication then modulates the amplitude and phase of that band. The fused spectrum is mapped to the future spectrum and inverted. The authors argue that this is the first frequency-based multimodal fusion for forecasting, and they provide experimental evidence that it consistently improves accuracy over time-domain fusion baselines while using far fewer parameters.

Load-bearing premise

The paper assumes that an arbitrary learned complex projection of text embeddings behaves like a true Fourier-domain signal, so that multiplying it with the series spectrum inherits convolution-theorem semantics; no Fourier transform is actually applied to the text.

Editorial extensions

If this is right

If this claim holds, any forecasting pipeline with access to free-form text can replace specialized time-domain alignment modules with a single lightweight frequency-domain operation.
The mechanism provides an interpretable notion of text influence: high-frequency bands capture immediate shocks, low-frequency bands capture trend shifts, and the model can selectively amplify only the relevant bands.
Parameter counts drop by an order of magnitude relative to some time-domain multimodal baselines, making the approach feasible for resource-constrained or high-throughput deployment.
The attention weights between documents and frequency bands could be inspected to explain which textual events affect which temporal scales, aiding model auditing.
Because the fusion block is agnostic to the language model used for text embedding, performance could improve further as language models become stronger.
If the model is correct, the same spectral-modulation idea could transfer to other exogenous modalities, such as images or metadata, giving a general multimodal forecasting recipe.

Reading between the lines

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

The paper never applies a Fourier transform to the text itself; the 'frequency' representation of text is obtained by a learned complex projection. A direct test would be to replace that projection with the FFT of a text-derived scalar sequence and compare—if the learned projection is essential, the convolution-theorem framing is not doing the work.
The Economy domain, where SpecTF loses to a time-domain baseline, suggests a boundary condition: noisy or highly local text signals may require step-wise alignment, so the frequency-domain advantage may be largest when text conveys slow, regime-level information.
One could test frequency-selectivity directly by masking out selected frequency bands after fusion and measuring whether performance degrades selectively on short-horizon versus long-horizon predictions, revealing whether the model truly uses multiscale information.
A natural extension would be to apply the same complex-multiplication fusion to other exogenous signals, such as image embeddings or discrete events, to see whether the frequency-domain mechanism generalizes beyond text.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Things you should know upfront. This is one of the first papers to fuse external text with time series in the frequency domain via cross-attention, and it ships code and a clean parameter-efficient design. The core mechanism, FreqCMF, does attention between spectral time-series queries and text keys, then modulates the spectrum by complex multiplication. That is a genuinely new combination, and the ablations show both parts matter: removing cross-attention hurts in Agriculture, removing multiplication fusion hurts in Health, and dropping text hurts broadly. The efficiency numbers are also real — 397K parameters on Energy versus 1.72M for TimeXer, with lower inference time. Worth reading for anyone doing multimodal forecasting.

The soft spots are mostly in the evidence, not the idea. The abstract says 'significantly outperforms,' but there are no standard deviations, confidence intervals, or paired tests anywhere, even though the checklist promises error bars in Appendix C. Appendix C just shows full tables without error bars. Several wins are small — Traffic MAE is tied with the best baseline, Security MSE is about 1% better than the runner-up — and the monthly datasets have only 297–900 samples, so those gaps can easily be seed noise. The tuning protocol is per-domain, and the sensitivity plots show strong responses to learning rate and dimension, notably for Security. So the average 3.82% MSE improvement needs verification. Economy goes the other way, and the tables have internal inconsistencies (e.g., the MM-TSF Economy and Climate values differ between Table 1 and the appendix). None of this sinks the method, but it does collapse the 'significant' claim unless seed-wise results and a fixed protocol are provided.

The theoretical appendix overreaches. Equation 7 projects text embeddings to complex vectors with two MLPs, no Fourier transform. Calling that a frequency representation is an architectural assumption, and the convolution theorem in A.2 doesn't directly apply to those vectors. That is fine as a learned fusion design, but the paper should stop presenting it as spectral alignment.

Bottom line: this deserves a serious referee. The architecture is novel, the empirical coverage is broad, and the code is promised. Ask for error bars, a pre-specified hyperparameter protocol, corrected tables, and softer wording. The central idea holds up; the evidence just needs to be made solid.

Referee Report

3 major / 6 minor

Summary. The paper proposes SpecTF, a frequency-domain fusion model for text-augmented time-series forecasting. It rFFTs a univariate lookback, projects spectral coefficients into complex embeddings, and fuses them with complex projections of per-timestep language-model embeddings via frequency cross-attention and complex multiplication. A FreqMLP maps fused history to future spectral coefficients, and irFFT returns predictions. Experiments on Time-MMD (9 domains) and TTC (2 datasets) compare against several multimodal baselines plus FreTS; the paper reports 8/9 domain improvements relative to the best multimodal baseline on Time-MMD, a 3.82% average MSE gain, better TTC results, lower parameter counts, ablations, and visualizations. The central claim is that explicit spectral fusion of text is more effective and more parameter-efficient than time-domain fusion.

Significance. If the empirical results hold, SpecTF is a useful, lightweight addition to multimodal forecasting: it is substantially smaller than TimeXer/MM-TSF/TaTS and it makes a clean design choice (spectral modulation) that is easy to build on. The ablation study and efficiency table are informative, and the code URL improves reproducibility. However, the manuscript currently overreaches: the claim of 'significant' improvement is not backed by variance estimates or significance tests, and the convolution-theorem justification for the text branch is not mathematically established. The core idea is plausible and worth publishing after these issues are fixed.

major comments (3)

[§5.1, Table 1, Appendix C, Checklist 3(c)] The abstract and §5.1 say SpecTF 'significantly outperforms' baselines, and the checklist promises error bars in Appendix C. No standard deviations, confidence intervals, or significance tests appear in the main text or Appendix C; only point averages over seeds are reported. This is load-bearing because several gains are small: Security MSE is 108.411 vs. 109.472 for TimeXer (0.97%), Traffic MAE ties at 0.210, and Economy is worse than TaTS. The monthly datasets contain only 297–900 samples, and the tuning protocol sweeps a prior weight over {0.1,0.2,0.4,0.5} with strong per-domain learning-rate and dimension sensitivities (Figs. 4–6). Please report seed-level statistics or CIs and run paired significance tests for the main comparisons, or soften 'significantly'.
[§4.2 Eq. (7), §4.3 Eq. (10), Appendix A.2 Eq. (12)] Appendix A.2 claims that the complex multiplication in Eq. (10) is a global time-domain convolution via the convolution theorem. The theorem requires both operands to be Fourier transforms of time-domain signals. Here the text branch never applies a Fourier transform: Eq. (7) maps per-timestep LM embeddings through two MLPs to arbitrary complex vectors, and the attention output \hat{O} is a nonlinear function of these vectors. There is no guarantee that \hat{O} equals \hat{S}(k) for some text signal, so Eq. (12) does not justify Eq. (10). The Parseval argument has the same issue. This should be corrected either by applying a genuine spectral transform to text or by reframing FreqCMF as a learned complex spectral modulation, not a literal convolution.
[Appendix C.1, Table 7] The full-results table is inconsistent with Table 1 and internally. For Climate, the FreTS MSE entries are 0.286/0.283/0.294/0.293, while Table 1 reports FreTS Climate MSE as 1.289; the MAE values (0.878–0.897) appear with these implausible MSE values. For Economy, ChatTime at horizon 6 is shown as 0.478, while the other ChatTime rows are ~0.056, suggesting a missing leading zero (0.0478). Since the appendix is cited as support for the averaged claims, these entries must be corrected and the averages re-verified.

minor comments (6)

[Appendix B.3, Eqs. (17)–(18)] MAE is defined with |y_i - x^p_i|^2; the square should be removed. The same typo appears in both equations.
[§3.3, Eq. (4)] The displayed equation has a stray parenthesis and an inconsistent use of \sigma; please clean up the notation for FreqMLP.
[§4.2, Eq. (7) and following text] The type of \hat{s}_t is written as \mathbb{C}^{L\times d}, but it should be a single d-dimensional complex vector; otherwise the subsequent stack [\hat{s}_1,\ldots,\hat{s}_L] has the wrong shape. Please fix the dimension bookkeeping.
[Appendix A.4, Eq. (14)] The time-domain multi-scale formulation uses vector-valued s(t) and h_k(t) without defining the convolution for vector signals. A short clarification or a scalar example would help.
[§2, Related Work] Text2Freq is discussed as the closest frequency-domain multimodal work but is not included in the experiments or efficiency comparison. If it is excluded, one sentence justifying that choice would strengthen the baseline section.
[Appendix C.3, Figs. 4–6] These hyperparameter plots appear to be point curves; if the reported main results are averages over seeds, adding per-seed error bars would let readers see the seed variability that is claimed but not reported.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: SpecTF is an empirical, benchmark-evaluated method; the only flagged issues are a non-derived text-frequency assumption and missing statistical support, neither of which is an input-output reduction.

full rationale

SpecTF's central claim is empirical: its MSE/MAE results on Time-MMD and TTC are obtained by training the model end-to-end and evaluating on held-out horizons against external baselines. I found no step where a fitted parameter is renamed as a prediction, no quantity defined in terms of the quantity it is supposed to explain, and no load-bearing self-citation. The only self-citation ([Le et al., 2025], Introduction) is an application-domain reference and is not used to justify the method. The convolution-theorem discussion in Appendix A.2 is a standard mathematical result applied to the time-series spectrum; it is not used to derive the empirical gains. The paper's weakest point is that text embeddings are mapped to complex vectors by MLPs (Eq. 7) without a Fourier transform, so the 'frequency' semantics of the text stream are an architectural assumption rather than a derived property. That is a modeling/interpretability limitation, not a circular reduction: the output is not equal to the input by construction. Separately, the checklist asserts error bars are in Appendix C, but the appendix reports only horizon-wise tables with no standard deviations, and the paper gives no significance tests; this undermines the strength of the 'significantly outperforms' wording but is a statistical-evidence issue, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical or mathematical entities. Its central load-bearing assumptions are domain-level (text has multiscale influence) and architectural (text can be treated as a frequency-domain multiplier). The only free parameters are standard hyperparameters, but they are tuned per dataset and could inflate the reported improvements.

free parameters (3)

model dimension d = not specified per domain; varied in Figure 5
Model capacity is tuned per dataset/domain (Figure 5), with domain-specific plateaus and Security showing minimal sensitivity; this tuning can affect reported gains.
learning rate = not specified; varied in Figure 4 (1e-5 to 5e-4 range)
Learning rate is tuned per domain; Security requires precise tuning to avoid MSE spikes, indicating the method is sensitive to this choice.
prior weight = chosen from {0.1, 0.2, 0.4, 0.5}
Table 5 lists a 'prior weight' hyperparameter chosen from a small set, but the paper does not explain what it weights or how it is selected across domains.

assumptions (5)

standard math Fourier transform, convolution theorem, and Parseval's theorem
Used in Appendix A to argue that frequency multiplication is global convolution and that no energy is lost; these are standard results and are correctly stated.
domain assumption Textual context exerts multiscale temporal influence on time series (high-frequency vs low-frequency components)
The motivating example in Section 1 (policy announcement causing short-term volatility and long-term trend) is an assumption about real-world text-time dynamics, not proven by the data.
ad hoc to paper Per-timestep language-model embeddings, after complex projection, can be treated as frequency-domain signals compatible with the time-series spectrum
Section 4.2 maps text embeddings to complex vectors with MLPs but applies no Fourier transform; the 'frequency' interpretation of text is introduced specifically for this architecture and is not independently established.
ad hoc to paper Complex multiplication of the time-series spectrum by the attention output is a valid way to reweight amplitude and phase
Eq. 10 defines this fusion, and Appendix A.1 justifies it via complex multiplication in general, but no result shows that text's influence on real time series is multiplicative in frequency.
domain assumption Channel-independent processing is sufficient
Section 4.1 explicitly adopts channel independence, ignoring multivariate interactions; this is a modeling choice that could limit performance on cross-variate datasets.

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Cite this review

Pith. "Pith review of Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting." pith.science (2026). https://pith.science/paper/HUNLCKHK

@misc{pith2026260201588,
  author       = {Pith},
  title        = {Pith review of: Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HUNLCKHK}},
  note         = {Machine review of arXiv:2602.01588}
}

read the original abstract

Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context embedded in other modalities, such as text. While most existing methods align textual features with time-series patterns one step at a time, they neglect the multiscale temporal influences of contextual information such as time-series cycles and dynamic shifts. This mismatch between local alignment and global textual context can be addressed by spectral decomposition, which separates time series into frequency components capturing both short-term changes and long-term trends. In this paper, we propose SpecTF, a simple yet effective framework that integrates the effect of textual data on time series in the frequency domain. Our method extracts textual embeddings, projects them into the frequency domain, and fuses them with the time series' spectral components using a lightweight cross-attention mechanism. This adaptively reweights frequency bands based on textual relevance before mapping the results back to the temporal domain for predictions. Experimental results demonstrate that SpecTF significantly outperforms state-of-the-art models across diverse multi-modal time series datasets while utilizing considerably fewer parameters. Code is available at https://github.com/hiepnh137/SpecTF.

Figures

Figures reproduced from arXiv: 2602.01588 by the authors.

**Figure 2.** An overview of the proposed SpecTF framework. The time series input is passed through Time Series Embedding to be encoded in the frequency domain, and concurrently, Text Embedding represents each document in the frequency domain. Frequency Cross-Modality Fusion (FreqCMF) integrates textual information into time series frequencies through attention mechanisms and multiplication fusion based on complex multiplication… view at source ↗

**Figure 3.** Visualization of frequency-text interactions in the Climate dataset. The attention map (center) reveals document-frequency relationships, with brightness indicating attention strength. Documents 13, 16, and 20 (left panel) show strong attention weights in middle-frequency bands (2-7), highlighted by the red rectangle. The frequency amplitude comparison (right) confirms this relationship: amplitudes after fusion (ora… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Parameter study on learning rate [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]

**Figure 5.** Figure 5: Parameter study on model dimension d [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]

**Figure 6.** Figure 6: Performance comparison of different language models. [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

ALER-TI: Aligned Latent Embedding Retrieval for Time Series Imputation
cs.LG 2026-07 conditional novelty 6.0 of 10

ALER-TI is a retrieval-augmented framework that aligns corrupted query representations with cached historical candidates via post-hoc latent masking, consistently improving time series imputation across multiple backbones.
Rethinking Multimodal Fusion for Time Series: Text Modalities Need Constrained Fusion
cs.LG 2026-03 unverdicted novelty 6.0 of 10

Uncontrolled text–time-series fusion underperforms unimodal baselines; constrained fusion and a low-rank Controlled Fusion Adapter recover gains without changing the TS backbone.

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Works this paper leans on

7 extracted references · 1 linked inside Pith · cited by 2 Pith papers

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[Yes, please refer to Appendix A] (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm

For all models and algorithms presented, check if you include: (a) A clear description of the mathematical set- ting, assumptions, algorithm, and/or model. [Yes, please refer to Appendix A] (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm. [Yes, the analysis of complexity is described in the Section 5] (c) (Opti...
[2]

[Yes, please refer to Appendix A] (b) Complete proofs of all theoretical results

For any theoretical claim, check if you include: (a) Statements of the full set of assumptions of all theoretical results. [Yes, please refer to Appendix A] (b) Complete proofs of all theoretical results. [Yes, please refer to Appendix A] (c) Clear explanations of any assumptions. [Yes, please refer to Appendix A]
[3]

[Yes, we provide source code, data and guidelines in the supplementary.] (b) All the training details (e.g., data splits, hy- perparameters, how they were chosen)

For all figures and tables that present empirical results, check if you include: (a) The code, data, and instructions needed to reproduce the main experimental results (ei- ther in the supplemental material or as a URL). [Yes, we provide source code, data and guidelines in the supplementary.] (b) All the training details (e.g., data splits, hy- perparamet...
[4]

[Yes] (b) The license information of the assets, if ap- plicable

If you are using existing assets (e.g., code, data, models) or curating/releasing new assets, check if you include: (a) Citations of the creator If your work uses ex- isting assets. [Yes] (b) The license information of the assets, if ap- plicable. [Yes] (c) New assets either in the supplemental mate- rial or as a URL, if applicable. [Not Applica- ble, we ...
[5]

[Not Applicable] (b) Descriptions of potential participant risks, with links to Institutional Review Board (IRB) approvals if applicable

If you used crowdsourcing or conducted research with human subjects, check if you include: (a) The full text of instructions given to partici- pants and screenshots. [Not Applicable] (b) Descriptions of potential participant risks, with links to Institutional Review Board (IRB) approvals if applicable. [Not Appli- cable] (c) The estimated hourly wage paid...

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ISBN 9781510860964

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ISSN 2227-7390. doi: 10.3390/math10213988. Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations, 2023. URLhttps://openreview. net/forum?id=Jbdc0vTOcol. Alec Radford, Jeff Wu, Rewon Child, David Luan, ...

arXiv 2023

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

[Yes, please refer to Appendix A] (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm

For all models and algorithms presented, check if you include: (a) A clear description of the mathematical set- ting, assumptions, algorithm, and/or model. [Yes, please refer to Appendix A] (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm. [Yes, the analysis of complexity is described in the Section 5] (c) (Opti...

[2] [2]

[Yes, please refer to Appendix A] (b) Complete proofs of all theoretical results

For any theoretical claim, check if you include: (a) Statements of the full set of assumptions of all theoretical results. [Yes, please refer to Appendix A] (b) Complete proofs of all theoretical results. [Yes, please refer to Appendix A] (c) Clear explanations of any assumptions. [Yes, please refer to Appendix A]

[3] [3]

[Yes, we provide source code, data and guidelines in the supplementary.] (b) All the training details (e.g., data splits, hy- perparameters, how they were chosen)

For all figures and tables that present empirical results, check if you include: (a) The code, data, and instructions needed to reproduce the main experimental results (ei- ther in the supplemental material or as a URL). [Yes, we provide source code, data and guidelines in the supplementary.] (b) All the training details (e.g., data splits, hy- perparamet...

[4] [4]

[Yes] (b) The license information of the assets, if ap- plicable

If you are using existing assets (e.g., code, data, models) or curating/releasing new assets, check if you include: (a) Citations of the creator If your work uses ex- isting assets. [Yes] (b) The license information of the assets, if ap- plicable. [Yes] (c) New assets either in the supplemental mate- rial or as a URL, if applicable. [Not Applica- ble, we ...

[5] [5]

[Not Applicable] (b) Descriptions of potential participant risks, with links to Institutional Review Board (IRB) approvals if applicable

If you used crowdsourcing or conducted research with human subjects, check if you include: (a) The full text of instructions given to partici- pants and screenshots. [Not Applicable] (b) Descriptions of potential participant risks, with links to Institutional Review Board (IRB) approvals if applicable. [Not Appli- cable] (c) The estimated hourly wage paid...

2025

[6] [2017]

ISBN 9781510860964

Curran Associates Inc. ISBN 9781510860964. Chengsen Wang, Qi Qi, Jingyu Wang, Haifeng Sun, Zirui Zhuang, Jinming Wu, Lei Zhang, and Jianxin Liao. Chattime: A unified multimodal time series foundation model bridging numerical and textual data. InAAAI Conference on Artificial Intelligence, 2025. Shiyu Wang, Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lin...

arXiv 2025

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doi: 10.3390/math10213988

ISSN 2227-7390. doi: 10.3390/math10213988. Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations, 2023. URLhttps://openreview. net/forum?id=Jbdc0vTOcol. Alec Radford, Jeff Wu, Rewon Child, David Luan, ...

arXiv 2023