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REVIEW 4 major objections 6 minor 41 references

TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that applying Kolmogorov-Arnold Networks directly to complex FFT coefficients, inside a dual-branch time-frequency architecture, yields consistently better long-term forecasts than eight state-of-the-art baselines on…

desk verdict Genuinely applies KAN in the frequency domain, but the SOTA claim is contradicted by its own table and the missing parameter-matched ablation leaves the core advantage unproven. read the letter →

arxiv 2506.12696 v1 pith:UZVOTRAX submitted 2025-06-15 cs.LG

Xiaoyan Kui , Canwei Liu , Qinsong Li , Zhipeng Hu , Yangyang Shi , Weixin Si , Beiji Zou This is my paper
classification cs.LG
keywords long-termtimeseriesforecastingKolmogorov-ArnoldNetworksfrequency-domainKANFastFourierTransformdual-brancharchitectureB-splineactivationperiodicpatternlearning
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 tries to establish that Kolmogorov-Arnold Networks (KANs) can be applied directly in the frequency domain, not just to raw time sequences, and that doing so improves long-term time series forecasting. It proposes TFKAN, a dual-branch network with a frequency-domain KAN operating on Fourier coefficients and a time-domain KAN operating on the raw series, fused through a KAN-based predictor. The paper reports that TFKAN outperforms eight strong baselines across seven datasets and multiple forecast horizons, with ablations showing that each branch and each KAN component contributes to the gain. If true, this would show that KAN's local B-spline activations are well matched to spectral structure, and that learnable function approximation on complex frequency components is a viable complement to time-domain modeling.

What carries the argument

The load-bearing mechanism is the frequency-domain KAN (FreqKAN), which applies KAN's base SiLU transformation and B-spline transformation to the real and imaginary components of complex FFT coefficients, sharing one KAN for both components. A dimension-adjustment step multiplies the input by a learnable vector of width $d=128$ only in the frequency branch, creating a richer spectral representation while leaving the time branch at its original width. The time-domain KAN processes the raw input, and the two branch outputs are combined with a bias term before a final KAN-based predictor maps the flattened hidden state to the forecast horizon $\tau$.

What would settle it

Train a parameter-matched TFKAN variant (for example, reduce the hidden size or spline grid so it has roughly 31K parameters, matching TimeKAN) on the same seven datasets and check whether it still beats TimeKAN and LTSF-Linear; if the gap disappears or reverses, the reported frequency-domain KAN advantage is not established. Equivalently, scale TimeKAN or LTSF-Linear up to about 16M parameters and see whether the margin shrinks.

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Extended reading notes

Core claim

The central claim is that placing KAN modules directly on the Fourier representation of a time series is both feasible and beneficial for long-term forecasting. The frequency-domain KAN processes the real and imaginary parts of the FFT output separately through a shared two-layer KAN, recombines them into a complex signal, and transforms back with the inverse FFT. Combined with a time-domain KAN branch and a selective upscaling strategy that enriches only the frequency path, this dual-branch design is reported to achieve the lowest MAE and RMSE on all tested datasets and horizons, beating frequency-domain MLPs, frequency-enhanced Transformers, and prior KAN hybrids. The paper presents this as the first direct application of KAN in the frequency domain for time series forecasting.

Load-bearing premise

The load-bearing premise is that the evaluation is fair: TFKAN (16.33M parameters) is compared against TimeKAN (31.1K) and LTSF-Linear (4.66K) with no parameter-matched ablation, so if extra capacity explains the gains, the frequency-domain KAN claim collapses.

Editorial extensions

If this is right

  • Frequency-domain KAN is a workable design: applying spline activations to Fourier coefficients improves accuracy over time-domain-only KAN baselines like TimeKAN.
  • The dual-branch structure is necessary: removing either the time or frequency branch degrades performance, indicating that temporal and spectral information are complementary.
  • Selective upscaling only in the frequency branch beats both no adjustment and full adjustment, suggesting that the two domains should be processed asymmetrically.
  • Sharing one KAN for the real and imaginary parts is sufficient; separate KANs add parameters with only marginal accuracy gains and impose a form of conjugate consistency.
  • TFKAN keeps GPU memory around 251 MB, far below Transformer-based baselines, while delivering the reported accuracy gains.

Reading between the lines

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

  • If the frequency-domain KAN advantage is real, it should transfer to pipelines that operate entirely on complex frequency components, such as interpolation-based complex spectral models, and the gain should persist when those pipelines are matched for parameter count.
  • The toy experiments suggest a testable hypothesis: KAN's advantage over MLPs should grow with the number of harmonics and phase shifts in the signal. A synthetic benchmark with known spectral sparsity could localize exactly where frequency-domain KAN helps.
  • A parameter-matched or FLOP-matched comparison is the missing control: TFKAN uses 16.33M parameters versus 31.1K for TimeKAN and 4.66K for LTSF-Linear, so the reported margins may reflect capacity rather than the frequency-domain KAN mechanism itself.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes TFKAN, a dual-branch architecture for long-term time series forecasting that combines a KAN operating on the frequency-domain representation of the input (FreqKAN) with a KAN operating on the raw time-domain signal (TimeKAN), followed by a KAN-based predictor. The frequency branch applies FFT, processes the real and imaginary parts with a shared two-layer KAN, then applies IFFT; a dimension-adjustment strategy embeds the frequency-branch input to a higher dimension while leaving the time-branch input unchanged. The authors claim this is the first direct application of KAN in the frequency domain for time series forecasting, and they report experiments on seven datasets (ETT, Air, Weather, ILI) comparing against eight baselines, together with ablations over KAN placement, single-branch variants, dimension adjustment, and parameter sensitivity. The main text asserts that TFKAN consistently outperforms all baselines on all datasets and horizons.

Significance. If the central claim were fully established, the contribution would be of moderate significance: it would demonstrate that KAN modules applied to complex FFT coefficients, combined with a time-domain KAN branch, improve long-term forecasting accuracy over existing KAN-based, frequency-based, and hybrid baselines. The paper has strengths that deserve credit: the code is publicly released, the ablation suite is fairly extensive, the efficiency table reports parameter counts and GPU memory, and the toy periodic-function experiment provides a concrete motivation for placing KAN in the frequency domain. However, the empirical evidence as presented is not yet sufficient to support the claimed consistent superiority, and the missing capacity-controlled comparison is load-bearing because TFKAN has orders of magnitude more parameters than the most relevant baselines. The significance of the result is therefore conditional on the authors addressing the evaluation gaps.

major comments (4)
  1. [Section IV-B / Table III] The claim in Section IV-B that "TFKAN achieves consistently superior results across all datasets and forecasting lengths" is contradicted by the paper's own Table III. For example, on ETTh1 with tau=336 the MAE for TimeKAN is 0.069 while TFKAN is 0.071; with tau=720 TimeKAN gives 0.080 vs TFKAN 0.082; and on ETTm1 with tau=192 TimeKAN gives 0.057 vs TFKAN 0.058. Several other cells are tied or within 0.001. The paper does not report standard deviations, confidence intervals, or multi-seed runs, so the aggregate "Num First" counts (21 vs 20 for MAE) cannot be interpreted as a statistically meaningful advantage. Please revise the claimed consistent superiority, report error bars or significance tests, and state explicitly which cells are and are not statistically distinguishable.
  2. [Section IV-A / Table VIII / Table IV] The reported gains may reflect model capacity rather than the benefit of frequency-domain KAN. Table VIII shows TFKAN has 16.33M parameters on ILI, while TimeKAN has 31.1K, LTSF-Linear has 4.66K, and TSMixer has about 215K. The KAN-vs-MLP ablation in Table IV does not remove this confound, because replacing a KAN layer with a two-layer MLP drastically reduces the parameter count; for instance, on ETTh2 with tau=720 the TFKAN MAE is 0.047 and the fully MLP variant is 0.060, but the two models are not parameter-matched. Without a comparison in which the MLP baseline is widened to match TFKAN's parameter budget, or a FLOP-matched comparison, the claim that applying KAN in the frequency domain is the cause of the accuracy advantage is not established. Please add parameter-matched or FLOP-matched experiments, or otherwise show that the improvements are not attributable to capacity alone.
  3. [Section IV-A / Table II / Table III] The evaluation omits several strong recent baselines that are standard in LTSF, including PatchTST, iTransformer, and TimeMixer. PatchTST and iTransformer in particular are widely reported to outperform several of the included baselines (e.g., Informer and Autoformer), so the statement that TFKAN outperforms "state-of-the-art methods" is not supported by the chosen comparison set. The authors should either add these models (or cite published results on the same datasets and horizons) or soften the SOTA claim to "outperforms the eight selected baselines." This is load-bearing because the paper's central empirical claim is about superiority to the state of the art, not merely to the eight implemented baselines.
  4. [Section III-C / Equations (5)-(8)] The dimension-adjustment strategy introduces an asymmetry between the two branches that is also a capacity difference: the frequency branch embeds the input to N x L x d (d=128), while the time branch processes the raw N x L input. Consequently, the frequency branch has substantially more representation capacity regardless of whether KAN or MLP is used, and the ablation "All Adjust" in Table VI does not isolate the frequency-domain KAN contribution because it applies upscaling to both branches. Please clarify, either by controlling total width/capacity across branches or by reporting an ablation that keeps the frequency-branch capacity fixed while varying only the use of KAN versus MLP, whether the reported Freq branch advantage is due to the KAN module or to the higher-dimensional embedding.
minor comments (6)
  1. [Equations (6)-(7)] Equations (6) and (7) present the Fourier transform and its inverse as continuous integrals, but the implementation uses the discrete FFT/IFFT on a finite sequence of length L. Please replace these with discrete summations or explicitly state that the continuous forms are illustrative; the current notation is mathematically inconsistent with the dimensions given, such as C^{(L/2+1) x d}.
  2. [Section IV-A] The text states that each KAN layer uses a hidden size of 258; given the embedding size d=128 and grid size s=2, this number looks like a typo (possibly 256). Please verify and correct.
  3. [Figures 3 and 4] The captions refer to orange, green, and blue lines/bars, but the printed figures appear to use a different color scheme or insufficient contrast. Also, Figure 3's caption says the bars represent MSE while the text says MAE; please align the caption, axis labels, and legend.
  4. [Section II / Section III-C] The name "TimeKAN" is used both for a baseline method (Ref. [22]) and for the time-domain KAN branch of TFKAN in Figure 2 and Section III-C, which is confusing. Please rename the branch, for example to Time-Domain KAN or T-KAN, to avoid ambiguity.
  5. [Section I / Figure 1] The toy experiment is presented as evidence that KAN's spline bases naturally adapt around spectral peaks, but Figure 1 shows only qualitative curves and no error metric or training setup (e.g., epochs, parameter counts, number of trials). A quantitative comparison with error bars would make the motivation more convincing.
  6. [Table IV caption] The caption lists variants "MLP time freq," "MLP pred freq," and "MLP pred time" without defining the naming convention in the text; please define exactly which modules are replaced by MLPs in each variant before the table is referenced.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: TFKAN is an empirical architecture paper whose claims are evaluated against external benchmarks, not derived from its own fitted values or self-citations.

full rationale

The paper does not present a derivation in which a claimed prediction is defined in terms of the fitted quantity. The toy experiment in Section I motivates frequency-domain KANs by showing that KAN approximates sinusoidal functions more smoothly than an MLP, but this is motivation, not a load-bearing circular reduction. The proposed architecture (Section III) combines a frequency-domain KAN, a time-domain KAN, a dimension-adjustment strategy, and a KAN-based predictor; the final forecast is produced by a trainable model and evaluated against held-out data (Table III), so the main empirical claim is checked against external benchmarks rather than being forced by construction. The ablations in Section IV-C compare KAN versus MLP variants and single-branch versus dual-branch configurations; these are component analyses, and although the parameter counts differ (Table VIII), that is a potential confound or fairness issue, not circularity. The paper cites prior KAN and time-series work, including TimeKAN [22], but none of these citations carry a load-bearing uniqueness claim by the present authors, and there is no self-citation chain that defines TFKAN's result in terms of its own prior output. Concerns about parameter-matched comparisons, multi-seed variance, and the 'consistently superior' statement exceeding some table cells are scientific-validity criticisms and do not constitute circularity under the defined criteria. Therefore, the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No invented entities. Free parameters are standard hyperparameters selected by hand and sensitivity experiments. The main domain assumption is that frequency-domain representation improves KAN learning for periodic time series, supported only by a qualitative toy experiment.

free parameters (4)
  • Embedding size d = 128
    Set by hand; sensitivity analysis (Fig. 4) shows d=128 balances accuracy and training time. All main results use d=128.
  • KAN grid size s = 2
    Chosen by hand in Section IV-A; no sensitivity analysis for s is reported.
  • KAN spline order k = 1
    Chosen by hand in Section IV-A; no sensitivity analysis for k is reported.
  • KAN hidden size = 258
    Chosen by hand in Section IV-A; no sensitivity analysis reported.
assumptions (4)
  • standard math Kolmogorov-Arnold representation theorem
    Used in Section III-B to justify the KAN architecture's univariate function decomposition.
  • domain assumption FFT of a real signal captures periodic patterns in a form suitable for learning
    Section I motivates frequency-domain KAN by asserting periodic patterns are more salient in the frequency domain; not formally proven.
  • domain assumption Shared KAN weights for real and imaginary parts preserve phase information
    Section III-C processes Re and Im with the same KAN and calls this 'conjugate consistency'; this is a design assumption with limited analysis.
  • ad hoc to paper The toy experiment (Fig. 1) demonstrates KAN's advantage for multi-harmonic functions
    The toy study is qualitative and not quantified; the claimed advantage of B-splines near spectral peaks is inferred, not measured.

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Cite this review

Pith. "Pith review of TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting." pith.science (2026). https://pith.science/paper/UZVOTRAX

@misc{pith2026250612696,
  author       = {Pith},
  title        = {Pith review of: TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UZVOTRAX}},
  note         = {Machine review of arXiv:2506.12696}
}
abstract

Kolmogorov-Arnold Networks (KANs) are highly effective in long-term time series forecasting due to their ability to efficiently represent nonlinear relationships and exhibit local plasticity. However, prior research on KANs has predominantly focused on the time domain, neglecting the potential of the frequency domain. The frequency domain of time series data reveals recurring patterns and periodic behaviors, which complement the temporal information captured in the time domain. To address this gap, we explore the application of KANs in the frequency domain for long-term time series forecasting. By leveraging KANs' adaptive activation functions and their comprehensive representation of signals in the frequency domain, we can more effectively learn global dependencies and periodic patterns. To integrate information from both time and frequency domains, we propose the $\textbf{T}$ime-$\textbf{F}$requency KAN (TFKAN). TFKAN employs a dual-branch architecture that independently processes features from each domain, ensuring that the distinct characteristics of each domain are fully utilized without interference. Additionally, to account for the heterogeneity between domains, we introduce a dimension-adjustment strategy that selectively upscales only in the frequency domain, enhancing efficiency while capturing richer frequency information. Experimental results demonstrate that TFKAN consistently outperforms state-of-the-art (SOTA) methods across multiple datasets. The code is available at https://github.com/LcWave/TFKAN.

Figures

Figures reproduced from arXiv: 2506.12696 by the authors.

Figure 1
Figure 1. Comparison of MLP and KAN in approximating periodic functions [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The overall architecture of TFKAN: (a) Dimension Adjustment Strategy is used to prepare the data [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Parameter sensitivity studies of the embedding size [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (2 more)
Figure 3
Figure 3. Figure 3: Parameter sensitivity studies of the input length [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 5
Figure 5. Figure 5: Visualizations of predictions (ground truth vs. predictions) on the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Pith tools

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