Pith. sign in

REVIEW 5 major objections 6 minor 51 references

FM-LLM: A frequency-enhanced mixture-of-experts framework for adapting LLMs to time series forecasting

T0 review · 5 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read A prompt-free, frequency-aware design lets a frozen large language model outperform prior methods on 59 of 78 time-series forecasting metrics.

desk verdict A plausible, prompt-free frequency-MoE recipe for frozen-LLM forecasting whose SOTA claim is currently undercut by unmatched baseline protocols and small but telling evaluation errors. read the letter →

arxiv 2608.11623 v1 pith:FRK3INRU submitted 2026-08-12 cs.LG cs.AIcs.NIeess.SP

Rentao Gu , Yihang Ding , Junjie Li , Yi Ding , Weijing Sang , Xiaoli Huo , Xin Qin , Yuefeng Ji This is my paper · ORCID
classification cs.LGcs.AIcs.NIeess.SP
keywords timeseriesforecastinglargelanguagemodelsfrequencydomainmixtureofexpertsFourieranalysisautoregressivefew-shotlearningzero-shottransfer
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

This paper claims that the usual recipe for adapting large language models (LLMs) to time-series forecasting—text-like prompts plus a shallow linear decoder—is both inefficient and blind to the spectral structure of the data. It introduces FM-LLM, which sends each patch through a Fourier Analysis Network before it enters a frozen LLM, so harmonic information arrives without any prompt, and then reconstructs predictions with a mixture-of-experts decoder whose shared Fourier experts rebuild the periodic backbone while routed standard experts handle irregular residuals. On eleven public benchmarks the authors report state-of-the-art results on 59 of 78 metrics, with average improvements of 5.3% in mean squared error and 5.6% in mean absolute error over the strongest autoregressive LLM baseline. If true, this would mean prompt-free, frequency-aware adaptation can make frozen LLMs both more accurate and far cheaper than prompt-based forecasters, while preserving few-shot and zero-shot transfer. The cost is that the model is still slower and heavier than non-LLM baselines such as PatchTST, though markedly lighter than prompt-based LLM alternatives.

What carries the argument

The load-bearing mechanism is constrained asymmetric coupling: a Fourier Analysis Network (FAN) spectral token aligner on the encoding side and a heterogeneous mixture-of-experts (MoE) decoder on the decoding side. FAN injects harmonic structure by projecting each patch through sine-cosine basis functions combined with a nonlinear activation, giving the frozen LLM numerically compatible spectral tokens without any textual prompt. The decoder then adds always-on FAN-equipped Fourier experts to top-$K$ routed standard feed-forward networks, with a bias-based load-balancing scheme and a sequence-wise balance loss to prevent expert collapse. A time-frequency hybrid loss supervises both temporal accuracy and spectral consistency, and training computes the loss only on the token immediately following the context window, using signal-decay weights $w_l = 1/\sqrt{l}$ to suppress error accumulation in autoregressive rollouts.

What would settle it

Run the strongest baselines (AutoTimes, PRADA, PatchTST, iTransformer) inside FM-LLM's exact protocol—672-step lookback, 96-length tokens, the same frozen backbone, seeds, and train/validation/test splits—and recompute M4 metrics with the standard MASE denominator instead of Eq. (28); if FM-LLM no longer wins a majority of the 78 metrics, the headline SOTA claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the modality gap between continuous time series and discrete LLM tokens is better bridged by explicit spectral structure than by textual prompts. FM-LLM tokenizes each channel into non-overlapping patches, projects each patch through a single-layer Fourier Analysis Network $FAN(x) = \phi_L \circ \cdots \circ \phi_1(x)$, where interior layers output $[\cos(W_p x)\,\Vert\,\sin(W_p x)\,\Vert\,\sigma(B_{\bar p}+W_{\bar p}x)]$, and feeds those harmonic embeddings into a frozen LLM. The LLM autoregressively predicts the next token embedding, and a constrained mixture-of-experts decoder reconstructs the time-domain token: shared Fourier experts with FAN layers rebuild the global periodic backbone, while top-$K$ routed standard feed-forward networks capture non-periodic residuals. Training minimizes a hybrid loss $\alpha L_{\mathrm{freq}} + \beta L_{\mathrm{time}} + \lambda L_{\mathrm{Bal}}$, with a discrete-Fourier-transform $\ell^1$ discrepancy enforcing spectral consistency, signal-decay-weighted MSE promoting short-horizon fidelity, and a sequence-wise balance regularizer preventing routing collapse. On that basis the authors report state-of-the-art results on 59 of 78 metrics across eleven benchmarks, average MSE and MAE improvements of 5.3% and 5.6% over AutoTimes, and robust 10% few-shot and zero-shot transfer.

Load-bearing premise

The central claim assumes the numbers quoted from other papers were produced under conditions close enough to FM-LLM's own runs that the differences reflect architecture rather than experimental setup; if that comparability fails, the 59-of-78 claim could dissolve.

Editorial extensions

If this is right

  • Prompt-based LLM forecasters pay a large inference penalty; FM-LLM runs at 143.48 ms/iter on the 720-step Traffic task versus 1056.0 ms/iter for Time-LLM, so prompt-free frequency alignment makes frozen-LLM forecasting practical at long horizons.
  • A single trained FM-LLM applies to multiple prediction lengths without retraining and adapts with about 8.68 million trainable parameters, fitting in roughly 6 GB of GPU memory.
  • With only 10% of training data, and in zero-shot dataset transfer, FM-LLM retains superior accuracy; the paper links few-shot difficulty to spectral divergence between the reduced and full training sets.
  • Expert specialization is structurally interpretable: the paper's visualizations show Fourier experts tracking the low-frequency backbone while routed experts handle high-frequency residuals, giving a mechanistic account of the accuracy gains.

Reading between the lines

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

  • I would not treat the 59/78 count as settled until the leading baselines are re-run under FM-LLM's exact protocol; the paper compares against many numbers taken from original publications, so part of the margin could reflect lookback, backbone, or training differences.
  • The constrained-asymmetry recipe—spectral structure only in shared experts, residuals only in routed experts—could be lifted out and applied to other frozen encoders, with the hybrid time-frequency loss acting as a general regularizer.
  • A clean ablation that keeps the MoE decoder and hybrid loss but replaces the FAN aligner with a linear projection would isolate how much of the gain truly comes from spectral token alignment.
  • The non-monotonic training-data trend the paper reports on ETTm2 suggests standard fixed splits can misrepresent scaling behavior; reporting multiple training fractions, as FM-LLM does for two datasets, would be a more informative convention.
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, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper introduces FM-LLM, a framework for adapting frozen LLMs to multivariate time-series forecasting without textual prompts. The model consists of three main components: a Fourier Analysis Network (FAN)-based spectral token aligner that maps time-series patches into harmonic representations, an asymmetric Mixture-of-Experts (MoE) decoder in which shared experts with FAN layers model periodic structure and routed standard-FFN experts model non-periodic residuals, and a hybrid time-frequency loss that combines a signal-decay-weighted MSE with a frequency-domain L1 loss plus an auxiliary expert-balance loss. The authors evaluate FM-LLM on long-horizon benchmarks (ETT, Electricity, Weather, Traffic, PEMS), the M4 short-term benchmark, few-shot (10%) and zero-shot transfer settings. They claim state-of-the-art performance on 59/78 metrics in the abstract, with average MSE/MAE improvements of 5.3%/5.6% over the strongest autoregressive LLM baseline (AutoTimes), and support the design with ablations, expert-load analyses, spectral analyses, efficiency comparisons, and a distribution-shift diagnosis.

Significance. If the empirical claims hold, the contribution is likely valuable: a prompt-free, frequency-aware frozen-LLM forecaster with a structural role separation in the decoder is a plausible and reasonably novel design, and the reported efficiency gains over prompt-based LLM baselines are practically relevant. The paper contains several genuine strengths: full hyperparameter tables (Table 2), a useful decomposition of expert roles in the decoder, a detailed ablation set (Tables 8–9), expert-load histograms (Figure 5), a distribution-shift diagnosis for the non-monotonic data-scale effect (Appendix D), and explicit reporting of GPU memory, latency, and trainable-parameter counts (Table 10). These elements make the submission more reproducible and falsifiable than many empirical time-series papers. However, the central state-of-the-art claim is currently not verifiable because the evaluation protocol is asymmetric between FM-LLM and the baselines, the headline metric counts are inconsistent between the abstract and the main text, and the MASE formula appears nonstandard. These issues are fixable, but they are load-bearing for the paper's main conclusion.

major comments (5)
  1. [Abstract vs. §4.2 and Table A.12] The headline SOTA claim is internally inconsistent: the abstract states 59 out of 78 evaluation metrics, while §4.2 reports 51 best scores across 70 metrics and Table A.12 shows '1st Count 51'. Table 3's '1st Count' row (11 for FM-LLM) neither matches 51 nor 59. In addition, the average improvement over AutoTimes is given as 5.20% MSE and 5.32% MAE in §4.2 but as 5.3% and 5.6% in the abstract. Because the state-of-the-art claim is the central result, every count must be reconciled, and each number must be traceable to a specific table and metric set.
  2. [§4.1.4, Tables 2–3, and Figure 4] The evaluation protocol is asymmetric and undermines the SOTA claim. FM-LLM is run with lookback L=672 and token length P=96, while baseline results are 'primarily' taken from original publications, where lookback lengths are commonly 96–512. The paper's own Figure 4, observation (4), shows that FM-LLM's MSE decreases substantially from T=384 to T=768, so lookback length is a known performance driver for this architecture; it cannot be treated as a cosmetic detail for baselines. For PEMS, §4.1.4 states that if the L=672 result does not exceed the original-paper result, the original result is retained, which gives baselines a 'best-of-two' advantage while FM-LLM is reported at a single setting. AutoTimes* is the only baseline explicitly re-run under the Llama3.2-1B backbone; other LLM baselines use their original backbones. A valid SOTA claim requires a matched-protocol rerun of all baselines under the same lookback, backbone, seeds, and preprocessing, or at least a demonstration that lookback length does not change the relative ordering.
  3. [§4.1.2, Eq. (28)] The MASE formula in Eq. (28) is nonstandard. The denominator is written as (1/(N-s)) * sum_{j=s+1}^N |y_j - y_{j-s}|, with N described as 'the length of one token, which is equal to P'. Standard MASE scales the forecast error by the mean absolute error of the in-sample seasonal naive forecasts computed over the training set, not over the forecast window. Computing the scaling factor on the forecast window itself can shift M4 MASE values relative to published baselines, and the M4 comparison in Table 4 is therefore not on an equal footing. The authors should either adopt the standard definition or justify the alternative and validate it against published M4 numbers for a baseline such as Naive2.
  4. [All result tables (Tables 3–7, A.12)] No error bars, confidence intervals, or multiple-seed results are reported anywhere. Several claimed improvements are extremely small: in Table A.12, on ETTh2-336 PatchTST achieves MSE/MAE 0.329/0.380 versus FM-LLM 0.361/0.395, and on ETTm1-336 PRADA achieves 0.350/0.384 versus FM-LLM 0.351/0.379 (essentially tied). Without variance estimates, the 'consistently outperforming' statement in §4.2 is not supported. I request mean and standard deviation over at least three seeds for FM-LLM and for the re-run baselines, and significance testing for close comparisons.
  5. [§2.1 and Tables 3–7] Several recent baselines are cited in the related work but absent from the experimental comparisons: TimeKAN [26], CVC [24], EV-STLLM [25], and TimeMixer [21]. Given the paper's claim to state-of-the-art performance, omitting all of these from the tables prevents the SOTA claim from being verified against the most current methods, including LLM-based (CVC, EV-STLLM) and KAN-based (TimeKAN) competitors. At least the LLM-based and KAN-based baselines should be added under the matched protocol.
minor comments (6)
  1. [Table 1] The sampling frequency of ETTh1 and ETTh2 is listed as '15 min', which contradicts the text in §4.1.1 where these datasets are described as sampled hourly. Correct this factual error.
  2. [Eq. (19)] The frequency-domain loss term F(w_l · a_{t+l}) is not fully specified: it is unclear over what length the DFT is computed, whether the same window length P is used for every l, and how the normalization of F is chosen. Please specify the DFT length, normalization, and how the weighting w_l interacts with the frequency-domain term.
  3. [Eq. (13) and surrounding text] The notation for the gating variable is inconsistent: Eq. (13) uses g_{i,k}, the text says 'g_k^i indicates the normalized gating value' and then 'gi,k denotes the pre-normalized gating score'. Please unify the symbols and distinguish normalized from pre-normalized gating values throughout.
  4. [§3.1, Eq. (1)] The problem-definition notation is inconsistent: the historical window is x_{1:T}, but the mapping is written as f: x_{1:T} -> \hat{x}_{L+1:L+F}, using L instead of T. Use the same symbol for the lookback length throughout.
  5. [Throughout] There are numerous typos and formatting artifacts, including 'adpts' in the Figure 1 caption, 'M4-Weakly' instead of 'M4-Weekly' in Table 1, 'A verage' in Table 4, and stray LaTeX braces in Eq. (24). A careful proofread is needed.
  6. [Table 3] The '1st Count' row is confusing: it is not clear whether the numbers count per-model best scores across all 70 metrics or across some other subset. The count in the caption and the text (51 best) should be reconciled and the row removed or relabeled.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-fulfilling spectral evidence; core SOTA claim is empirical and not circular.

  1. self definitional [Section 4.8 (Spectral Analysis of Model Predictions), building on Section 3.3 Eq. (19)]
    "We observe that FM-LLM aligns better with the dominant frequency components and preserves the harmonic structure more faithfully, which is consistent with its frequency-enhanced token adaptation design."

    This passage offers spectral fidelity as evidence that the frequency-aware design works, but the training objective in Eq. (19) explicitly contains the frequency-domain term α·(1/L)Σ_l ||F(w_l·Rhat a_{t+l}) − F(w_l·a_{t+l})||_1, which directly penalizes mismatch between predicted and ground-truth Fourier coefficients. The observed spectral alignment is therefore not an independent emergent discovery; it is a direct consequence of the optimized loss. The claim that the result is 'consistent with its frequency-enhanced token adaptation design' is in this respect partly tautological. This does not affect the paper's main empirical SOTA comparison, which rests on time-domain MSE/MAE benchmark runs.

full rationale

The paper's central claim is empirical: FM-LLM is trained and evaluated on public benchmarks, and the SOTA assertion is based on reported MSE/MAE numbers. No fitted constant is renamed as a prediction, no load-bearing self-citation chain appears, and no uniqueness theorem is imported from the authors' prior work. The only circular-adjacent element is Section 4.8, where spectral consistency is presented as evidence of effectiveness even though the hybrid loss in Eq. (19) explicitly minimizes Fourier-coefficient mismatch, making that particular evidence partly self-fulfilling. Since this observation is not load-bearing for the headline SOTA claim, the overall circularity score is low rather than moderate or high.

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

The paper introduces no new physical entities. The Fourier expert and routed expert are architectural modules, not invented entities in the sense of new particles or forces. The main burden comes from per-dataset hyperparameters and the assumption that external baseline numbers are comparable.

free parameters (6)
  • loss weights alpha, beta, lambda = alpha: 0.9 or 1.0; beta: 1.0; lambda: 0.1 or 1.0 (Table 2)
    Tuned manually per dataset on validation set, affecting all reported results.
  • number of Fourier experts = 2 for all datasets (Table 2)
    Chosen via sensitivity analysis on ETTm1; set to 2.
  • number of routed experts = 2, 3, 6, or 8 depending on dataset (Table 2)
    Tuned per dataset; ETTh1 uses 2, ETT uses 3, high-dimensional datasets use 8.
  • top-K routed experts = 1, 2, or 3 depending on dataset (Table 2)
    Tuned per dataset; affects decoder capacity and routing sparsity.
  • learning rate, dropout, batch size = lr 1e-4 to 1e-3; dropout 0.0 to 0.2; batch 16 to 256 (Table 2)
    Standard hyperparameters tuned per dataset; no sensitivity analysis reported for these.
  • signal decay weights w_l = w_l = 1/sqrt(l)
    Chosen heuristic for loss weighting; not derived or compared to alternatives.
assumptions (5)
  • domain assumption Frozen LLM parameters encode transferable inductive biases for time-series forecasting.
    Central to the few-shot and zero-shot claims; supported only by the paper's own ablations (Table 9).
  • domain assumption Fourier basis functions are an appropriate inductive bias for the datasets tested.
    The whole method assumes harmonic decomposition captures the periodic backbone; no theoretical justification is given.
  • domain assumption Published baseline numbers are directly comparable under the paper's evaluation protocol.
    Section 4.1.3 uses results reported in original publications; baselines are not re-run under identical settings.
  • ad hoc to paper The MASE formula in Eq. (28) equals the standard MASE used by baselines and the M4 competition.
    Eq. (28) computes the denominator over the forecast window rather than the training sample's seasonal naive errors, which is nonstandard and likely invalidates M4 comparisons.
  • domain assumption Channel-wise independence in patching is appropriate for these datasets.
    Section 3.2.1 adopts channel-wise independence following PatchTST; no ablation is provided to justify it here.

how reviews work

0 comments
Cite this review

Pith. "Pith review of FM-LLM: A frequency-enhanced mixture-of-experts framework for adapting LLMs to time series forecasting." pith.science (2026). https://pith.science/paper/FRK3INRU

@misc{pith2026260811623,
  author       = {Pith},
  title        = {Pith review of: FM-LLM: A frequency-enhanced mixture-of-experts framework for adapting LLMs to time series forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FRK3INRU}},
  note         = {Machine review of arXiv:2608.11623}
}
read the original abstract

Recent advances in Large Language Models (LLMs) have spurred cross-modal solutions for time-series forecasting. However, existing methods rely heavily on textual prompts for modality alignment-introducing nontrivial computational overhead and failing to leverage the rich spectral dynamics inherent in time-series data. To enable prompt-free, frequency-aware adaptation of frozen LLMs, we propose FM-LLM (Frequency-Enhanced Mixture-of-Experts for adapting LLMs to Time Series Forecasting), an autoregressive framework grounded in constrained asymmetric coupling. A Fourier Analysis Network (FAN)-based spectral token aligner injects structured harmonic representations directly into the frozen LLM with numerical compatibility. An asymmetric Mixture-of-Experts (MoE) decoder enforces role separation: shared experts with lightweight FAN layers reconstruct the global periodic backbone, while routed experts-restricted to standard FFNs-specialize in modeling non-periodic residual dynamics. A time-frequency hybrid loss function jointly optimizes temporal accuracy and spectral consistency, mitigating error accumulation during long-horizon autoregressive rollouts. Evaluated across eleven public benchmarks, FM-LLM achieves state-of-the-art performance on 59 out of 78 evaluation metrics. Compared to the strongest autoregressive LLM-based baseline, it delivers average improvements of 5.3% in MSE and 5.6% in MAE, with maximum gains reaching 8.0% for MSE and 8.4% for MAE. FM-LLM also demonstrates robust transferability, maintaining superior performance in 10% few-shot and zero-shot forecasting scenarios.

Figures

Figures reproduced from arXiv: 2608.11623 by the authors.

Figure 1
Figure 1. An example to illustrate how FM-LLM adpts large lan [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. The input time series is first divided into tokens, w [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. The case study on ETT datasets. For convenience, we [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Analysis of hyperparameter sensitivity on ETTm1 d [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]
Figure 5
Figure 5. Figure 5: Expert load histograms across different datasets. [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]
Figure 6
Figure 6. Figure 6: Results on various percentages of ETTh1 and ETTm2. [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]
Figure 7
Figure 7. Figure 7: Token-wise frequency energy proportion comparis [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]
Figure 8
Figure 8. Figure 8: Frequency Response Analysis on Traffic Datasets [PITH_FULL_IMAGE:figures/full_fig_p026_8.png]
Figure 9
Figure 9. Figure 9: Visualization of Expert Specialization [PITH_FULL_IMAGE:figures/full_fig_p027_9.png]
Figure 10
Figure 10. Figure 10: Temporal Dynamics of Top-3 Expert Routing [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]
Figure 11
Figure 11. Figure 11: Prediction spectrogram cases from ETTh1 by groun [PITH_FULL_IMAGE:figures/full_fig_p029_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 33 canonical work pages

  1. [26]

    Huang, Z

    S. Huang, Z. Zhao, C. Li, L. BAI, TimeKAN: KAN-based freq uency de- composition learning architecture for long-term time seri es forecasting, in: International Conference on Learning Representations, 20 25

    work page

  2. [24]

    F. Li, H. Xu, H. Xu, Y. Liu, X. Ding, Cvc: Further aligning llms via cross-view correction for ti me series forecasting, Knowledge-Based Systems 326 (2025) 113957. doi:https://doi.org/10.1016/j.knosys.2025.113957. URL https://www.sciencedirect.com/science/article/pii/S0950705125010020

    arXiv 2025

  3. [25]

    H. Fan, Y. Chai, C. Liu, et al., Ev-stllm: Electric vehic le charging forecast- ing based on spatio-temporal large language models with mul ti-frequency and multi-scale information fusion, Expert Systems with Ap plications 313 (2026) 131620

    work page 2026

  4. [21]

    S. Wang, H. Wu, X. Shi, T. Hu, H. Luo, L. Ma, J. Y. Zhang, J. Z HOU, Timemixer: Decomposable multiscale mixing for time series forecasting, in: International Conference on Learning Representations, 20 24

    work page

  5. [1]

    Gonçalves, R

    C. Gonçalves, R. J. Bessa, T. Teixeira, J. Vinagre, Budge t-constrained collaborative renewable energy forecasting market, IEEE T rans. Sustain. Energy 16 (2) (2025) 1440–1452. doi:10.1109/TSTE.2025.3532835

    arXiv 2025

  6. [2]

    L. Zhao, Y. Song, C. Zhang, Y. Liu, P. Wang, T. Lin, M. Deng, H. Li, T-gcn: A temporal graph convolutional network for tra ffic pre- diction, IEEE Trans. Intell. Transp. Syst. 21 (9) (2019) 384 8–3858. doi:10.1109/TITS.2019.2935152

    arXiv 2019

  7. [3]

    Fiandrino, E

    C. Fiandrino, E. P. Gómez, P. F. Pérez, H. Mohammadalizad eh, M. Fiore, J. Widmer, Aichronolens: advancing explainability for tim e series ai forecasting in mobile networks, in: IEEE INFOCOM 2024-IEEE Con- ference on Computer Communications, IEEE, 2024, pp. 1521–1 530. doi:10.1109/INFOCOM52122.2024.10621134

    arXiv 2024

  8. [4]

    Kochkov, J

    D. Kochkov, J. Yuval, I. Langmore, P. Norgaard, J. Smith, G. Moo- ers, M. Klöwer, J. Lottes, S. Rasp, P. Düben, S. Hatfield, P. Ba ttaglia, A. Sanchez-Gonzalez, M. Willson, M. P. Brenner, S. Hoyer, Ne ural gen- eral circulation models for weather and climate, Nature 632 (8027) (2024) 1060–1066. doi:10.1038/s41586-024-07744-y

    doi:10.1038/s41586-024-07744-y 2024

Show all 51 references
  1. [5]

    Brown, B

    T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dh ariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, S. Agarwal, A . Herbert- Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh, D. Ziegle r, J. Wu, C. Winter, C. Hesse, M. Chen, E. Sigler, M. Litwin, S. Gray, B....

    2020

  2. [6]

    Y. Liu, G. Qin, X. Huang, J. Wang, M. Long, Autotimes: Auto regressive time series forecasters via large language models, Adv. Neu ral Inf. Process. Syst. 37 (2024) 122154–122184

    2024

  3. [7]

    S. Yin, C. Fu, S. Zhao, K. Li, X. Sun, T. Xu, E. Chen, A survey on multimodal large language models, Natl. Sci. Rev 11 (12) (20 24) nwae403. doi:https://doi.org/10.1093/nsr/nwae403

    doi

  4. [8]

    Y. Liu, Z. Kuang, H. Zhang, C. Li, F. Li, X. Ding, Prada: Prompt-guided representation alignment and dynamic adapt ion for time series forecasting, Knowl.-based Syst. 318 (2025) 113478. doi:https://doi.org/10.1016/j.knosys.2025.113478

    2025

  5. [9]

    T. Zhou, P. Niu, L. Sun, R. Jin, et al., One fits all: Power ge neral time series analysis by pretrained lm, Adv. Neural Inf. Process. Syst. 36 (2023) 43322–43355. 35

    2023

  6. [10]

    M. Jin, S. Wang, L. Ma, Z. Chu, J. Y. Zhang, X. Shi, P.-Y. Ch en, Y. Liang, Y.-F. Li, S. Pan, Q. Wen, Time-LLM: Time series forecasting b y repro- gramming large language models, in: International Confere nce on Learning Representations, 2024

    2024

  7. [11]

    T. Zhou, Z. Ma, Q. Wen, X. Wang, L. Sun, R. Jin, Fedformer: Frequency enhanced decomposed transformer for long-term series fore casting, in: Pro- ceedings of the 39th International Conference on Machine Le arning, PMLR, 2022, pp. 27268–27286

    2022

  8. [12]

    H. Wu, T. Hu, Y. Liu, H. Zhou, J. Wang, M. Long, Timesnet: T emporal 2d-variation modeling for general time series analysis, in : International Conference on Learning Representations, 2023

    2023

  9. [13]

    Y. Dong, G. Li, Y. Tao, X. Jiang, K. Zhang, J. Li, J. Deng, J . Su, J. Zhang, J. Xu, Fan: Fourier analysis networks, arXiv preprint arXiv :2410.02675 (2024)

    2024

  10. [14]

    G. E. Box, D. A. Pierce, Distribution of residual autoco r- relations in autoregressive-integrated moving average ti me se- ries models, J. Am. Stat. Assoc. 65 (332) (1970) 1509–1526. doi:10.1080/01621459.1970.10481180

    1970

  11. [15]

    E. S. Gardner Jr, Exponential smoothing: The state of th e art, J. Fore- casting 4 (1) (1985) 1–28

    1985

  12. [16]

    D. B. Percival, A. T. Walden, Spectral analysis for phys ical applications, cambridge university press, 1993. doi:10.1017/CBO9780511622762

    1993 doi

  13. [17]

    H. Wang, J. Peng, F. Huang, J. Wang, J. Chen, Y. Xiao, Micn : Multi- scale local and global context modeling for long-term serie s forecasting, in: International Conference on Learning Representations, 20 23

  14. [18]

    W. Cai, Y. Liang, X. Liu, J. Feng, Y. Wu, Msgnet: Learning multi-scale inter-series correlations for multivariate time series fo recasting, in: Pro- ceedings of the AAAI Conference on Artificial Intelligence, Vol. 38, 2024, pp. 11141–11149

    2024

  15. [19]

    C. Li, H. Zhang, S. Abbas, C. Ma, Y. Liu, X. Tu, Panda: Patc h- aware graph network with dual alignment for time series fore cast- ing, in: ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2025, pp . 1–5. doi:10.1109/ICASSP4...

    2025

  16. [20]

    A. Zeng, M. Chen, L. Zhang, Q. Xu, Are transformers effect ive for time series forecasting?, in: Proceedings of the AAAI Conferenc e on Artificial Intelligence, Vol. 37, 2023, pp. 11121–11128. 36

    2023

  17. [22]

    Y. Nie, N. H. Nguyen, P. Sinthong, J. Kalagnanam, A time s eries is worth 64 words: Long-term forecasting with transformers, in: Int ernational Con- ference on Learning Representations, 2023

    2023

  18. [23]

    Y. Liu, T. Hu, H. Zhang, H. Wu, S. Wang, L. Ma, M. Long, itra nsformer: Inverted transformers are effective for time series forecas ting, in: Interna- tional Conference on Learning Representations, 2024

    2024

  19. [27]

    Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. So ljačić, T. Y. Hou, M. Tegmark, Kan: Kolmogorov-arnold networks, in: Inte rnational Conference on Learning Representations, 2025

    2025

  20. [28]

    Gallant, White, There exists a neural network that does not make avoidable mistakes, in: IEEE 1988 International Conference on Neural Networks, IEEE, 1988, pp. 657–664. doi:10.1109/ICNN.1988.23903

    1988

  21. [29]

    W. Zuo, L. Cai, Tracking control of nonlinear systems us ing fourier neu- ral network, in: Proceedings of the 2005 IEEE/ASME Internat ional Con- ference on Advanced Intelligent Mechatronics, IEEE, 2005, pp. 670–675. doi:10.1109/AIM.2005.1511059

    2005

  22. [30]

    W. Zuo, L. Cai, Adaptive-fourier-neural-network-bas ed control for a class of uncertain nonlinear systems, IEEE Trans. Neural Netw. 19 (10) (2008) 1689–1701. doi:10.1109/TNN.2008.2001003

    2008

  23. [31]

    Ziyin, T

    L. Ziyin, T. Hartwig, M. Ueda, Neural networks fail to le arn periodic func- tions and how to fix it, Adv. Neural Inf. Process. Syst. 33 (202 0) 1583–1594

  24. [32]

    Uteuliyeva, A

    M. Uteuliyeva, A. Zhumekenov, R. Takhanov, Z. Assylbek ov, A. J. Castro, O. Kabdolov, Fourier neural networks: A comparative study, Intell. Data Anal. 24 (5) (2020) 1107–1120. doi:10.3233/IDA-195050. 37

    2020 doi

  25. [33]

    Sitzmann, J

    V. Sitzmann, J. Martel, A. Bergman, D. Lindell, G. Wetzs tein, Implicit neural representations with periodic activation function s, Adv. Neural Inf. Process. Syst. 33 (2020) 7462–7473

    2020

  26. [34]

    A. Q. Jiang, A. Sablayrolles, A. Roux, A. Mensch, B. Sava ry, C. Bamford, D. S. Chaplot, D. d. l. Casas, E. B. Hanna, F. Bressand, et al., Mixtral of experts, arXiv preprint arXiv:2401.04088 (2024)

    2024 arXiv

  27. [35]

    Fedus, B

    W. Fedus, B. Zoph, N. Shazeer, Switch transformers: Sca ling to trillion parameter models with simple and efficient sparsity, J. Mach. Learn. Res. 23 (120) (2022) 1–39

    2022

  28. [36]

    A. Liu, B. Feng, B. Xue, B. Wang, B. Wu, C. Lu, C. Zhao, C. De ng, C. Zhang, C. Ruan, et al., Deepseek-v3 technical report, arX iv preprint arXiv:2412.19437 (2024)

    2024 arXiv

  29. [37]

    W. Xue, T. Zhou, Q. Wen, J. Gao, B. Ding, R. Jin, Card: Chan nel aligned robust blend transformer for time series forecasting, in: I nternational Con- ference on Learning Representations, 2024

    2024

  30. [38]

    Hounie, J

    I. Hounie, J. Porras-Valenzuela, A. Ribeiro, Loss shap ing constraints for long-term time series forecasting, in: Proceedings of the 4 1st International Conference on Machine Learning, PMLR, 2024, pp. 19062–1908 4

    2024

  31. [39]

    H. Wang, L. Pan, Z. Chen, D. Yang, S. Zhang, Y. Yang, X. Liu , H. Li, D. Tao, Fredf: Learning to forecast in the frequency domain, in: Interna- tional Conference on Learning Representation, 2025

    2025

  32. [40]

    N. Du, Y. Huang, A. M. Dai, S. Tong, D. Lepikhin, Y. Xu, M. K rikun, Y. Zhou, A. W. Yu, O. Firat, et al., Glam: Efficient scaling of la nguage models with mixture-of-experts, in: Proceedings of the 39t h International Conference on Machine Learning, PMLR, 2022, pp. 5547–5569

    2022

  33. [41]

    Devlin, M.-W

    J. Devlin, M.-W. Chang, K. Lee, K. Toutanova, Bert: Pre- training of deep bidirectional transformers for language understanding, i n: Proceedings of the 2019 conference of the North American chapter of the asso ciation for computational linguistics: human language technologies...

    2019 doi

  34. [42]

    Radford, J

    A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, I. Sutske ver, Language models are unsupervised multitask learners, OpenAI Blog 1 ( 8) (2019)

    2019

  35. [43]

    Goerg, Forecastable component analysis, in: Procee dings of the 30th International Conference on Machine Learning, Vol

    G. Goerg, Forecastable component analysis, in: Procee dings of the 30th International Conference on Machine Learning, Vol. 28 of Pr oceedings of Machine Learning Research, PMLR, 2013, pp. 64–72

    2013

  36. [44]

    S. Lin, H. Chen, H. Wu, C. Qiu, W. Lin, Temporal query netw ork for efficient multivariate time series forecasting, in: Proceed ings of the 42nd International Conference on Machine Learning, 2025. 38

    2025

  37. [45]

    Y. Liu, H. Wu, J. Wang, M. Long, Non-stationary transformers: Exploring the stationarity in time series forecasting, in: Adv. Neural Inf. Process. Syst., Vol. 35, 2022. URL http://papers.nips.cc/paper_files/paper/2022/hash/4054556fcaa934b0bf76da52cf4f92cb-Ab

    2022

  38. [46]

    Kitaev, Ł

    N. Kitaev, Ł. Kaiser, A. Levskaya, Reformer: The efficien t transformer, in: International Conference on Learning Representations , 2020. doi:10.48550/arXiv.2001.04451. URL https://openreview.net/forum?id=rkgNKkHtvB

    2020 doi arXiv

  39. [47]

    Y. Hu, P. Liu, P. Zhu, D. Cheng, T. Dai, Adaptive multi-sc ale decompo- sition framework for time series forecasting, in: Proceedi ngs of the AAAI Conference on Artificial Intelligence, Vol. 39, 2025, pp. 17 359–17367

    2025

  40. [48]

    S. Lin, W. Lin, X. Hu, W. Wu, R. Mo, H. Zhong, Cyclenet: enh ancing time series forecasting through modeling periodic pattern s, Adv. Neural Inf. Process. Syst. 37 (2024) 106315–106345

    2024

  41. [49]

    B. N. Oreshkin, D. Carpov, N. Chapados, Y. Bengio, N-beats: Neural basis expansion analysis for interpretabl e time series forecasting, in: International Conference on Learning Representations , 2020. doi:10.48550/arXiv.1905.10437. URL https://openreview.net/forum?id=r1ecqn4YwB

    2020 doi arXiv

  42. [50]

    Challu, K

    C. Challu, K. G. Olivares, B. N. Oreshkin, F. Garza, M. Me rgenthaler- Canseco, A. Dubrawski, Nhits: Neural hierarchical interpo lation for time series forecasting, in: Proceedings of the AAAI Conference on Artificial In- telligence, Vol. 37, 2023, pp. 6989–6997. doi:10.1609/aa...

    2023 doi

  43. [51]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. C hanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al., Pytorch : an imperative style, high-performance deep learning library, Adv. Neura l Inf. Process. Syst. 32 (2019) 8026–8037. 39

    2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.