REVIEW 4 major objections 7 minor 6 cited by
TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting
T0 review · 4 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash
Pith's one-line read A 12K–38K-parameter network outperforms million-parameter forecasters on five benchmarks.
desk verdict TimeKAN is a clean, lightweight KAN-based frequency decomposition model with real efficiency gains, but its SOTA claim rests on baseline results whose comparability the paper never demonstrates. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing mechanism is the Decomposition-Learning-Mixing loop built from three blocks. Cascaded Frequency Decomposition (CFD) blocks obtain each frequency band's series representation as a residual: moving averages strip high frequencies level by level, then Frequency Upsampling -- an FFT, zero-padding to the longer length, and inverse FFT -- brings a lower-level sequence back to the upper level's length without changing its frequency content, so the band is $f_i = x_i - \hat{x}_i$. Multi-order KAN Representation Learning (M-KAN) blocks then model each band with a ChebyshevKAN whose polynomial order $b + k - i$ increases from low to high frequencies, plus a depthwise convolution that captures temporal dependencies channel-by-channel; the two branches' outputs are added. Frequency Mixing blocks recombine the learned bands by reversing the upsampling, so the whole decomposition-learning-mixing process can be repeated $L$ times before a final linear map produces the forecast. The key identity the architecture leans on is that zero-padded FFT/IFFT upsampling is lossless in frequency content, which is what makes the residual bands well-defined.
What would settle it
Rerun all twelve baselines in Table 1 under one shared protocol -- same data splits, normalization, seeds, and hyperparameter tuning -- with look-back T=96 and prediction lengths {96,192,336,720}. If TimeKAN no longer holds the best average MSE on at least five of the six datasets, or if TimeMixer or iTransformer ties it under identical training conditions, the state-of-the-art claim is falsified. A secondary check: independently reproduce Table 8's Electricity result at T=512 to see whether TimeKAN's reported advantage over TimeMixer and MOMENT survives.
Extended reading notes
Core claim
TimeKAN's central claim is that mixed-frequency time series are best handled by decoupling frequencies first, then learning each frequency band with a KAN whose expressiveness is tuned to that band, rather than by applying one uniform network to the whole series. Concretely, low-frequency bands (long-term trends) get low-order Chebyshev KANs and high-frequency bands (abrupt, information-dense patterns) get high-order KANs, while depthwise convolution learns temporal dependencies inside each band. The authors report that this Decomposition-Learning-Mixing architecture achieves the best average MSE/MAE on ETTh1, ETTh2, ETTm1, ETTm2, and Weather, and is second only to iTransformer on Electricity, with parameter counts from 12.84K to 38.12K and MACs far below PatchTST, iTransformer, TimeMixer, and the other baselines. On Electricity at the default T=96 window it trails iTransformer, which the paper attributes to the short window supplying too few effective frequency components; with a 512-step window, TimeKAN reports the best results on that dataset. The paper further argues via ablations that the FFT zero-padding upsampling is irreplaceable because it preserves frequency content, and that fixed-order KANs or MLPs are inferior to the increasing-order scheme.
Load-bearing premise
The result stands on the assumption that the baseline numbers in Table 1 were produced under the same data splits, normalization, and training conditions as TimeKAN; the paper states equal look-back and prediction lengths but does not say whether the baselines were re-run rather than copied from prior papers.
Editorial extensions
If this is right
- Forecasting accuracy does not require large parameter counts: TimeKAN's 12–38K parameters match or beat models with millions of parameters on five of six benchmarks, so future long-term forecasting can run with far smaller compute budgets.
- Frequency-band-specific capacity matters: assigning higher-order KANs to higher-frequency bands outperforms both fixed low-order and fixed high-order KANs, so treating all frequencies uniformly is a measurable handicap.
- Non-parametric frequency-preserving upsampling is load-bearing: replacing the FFT zero-padding upsample with linear interpolation, transposed convolution, or linear mapping degrades results, so the decomposition step should keep frequency content intact.
- Longer look-back windows compound the benefit: TimeKAN's error keeps falling as T grows, and on Electricity the model overtakes strong baselines when the window is extended from 96 to 512, indicating that frequency-based models are information-hungry.
- Depthwise convolution is the right temporal-dependency learner: it beats self-attention and standard convolution inside the M-KAN block, suggesting channel-independent temporal convolution is sufficient when each frequency band is modeled separately.
Reading between the lines
- Outside the paper: the order-matching principle (higher frequency bands get higher-order basis functions) may generalize to other basis families, such as Fourier features or Legendre polynomials, yielding similar gains when data has known spectral structure.
- Outside the paper: a testable extension is to make the per-band KAN order adaptive or learned rather than fixed by index, which could remove the need to tune the band count and the lower bound $b$.
- Outside the paper: because TimeKAN is variate-independent, combining it with a cheap cross-variate module, such as iTransformer's attention or a covariance layer, might close the remaining Electricity gap at T=96 while staying lightweight.
- Outside the paper: the frequency-decomposition view implies a diagnostic -- if a dataset's effective frequency count grows with window length, TimeKAN-style models should benefit more from longer look-back than linear or patch models, and practitioners can test this on their own series.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes TimeKAN, a variate-independent architecture for multivariate long-term time series forecasting. The model decomposes an input series into multiple frequency bands through cascaded moving-average downsampling and FFT-based upsampling, learns each band with a Multi-order KAN branch (ChebyshevKAN with increasing polynomial order) together with depthwise convolution, and recombines the bands through frequency mixing. Experiments are reported on ETTh1, ETTh2, ETTm1, ETTm2, Weather, and Electricity for look-back T=96 and horizons 96, 192, 336, and 720. The paper claims state-of-the-art accuracy with an extremely lightweight model (12.84K-38.12K parameters), and supports this with a main results table, ablations, an efficiency table, and repeated-seed statistics against one baseline.
Significance. If the empirical claims hold, the contribution is a useful lightweight alternative to much larger transformer- and MLP-based forecasters, and the Decomposition-Learning-Mixing framework with multi-order KANs is a plausible design contribution. Strengths include the public code release, component-level ablations, an efficiency comparison, and some repeated-seed analysis. However, the headline state-of-the-art claim is currently supported mainly by a single comparison table whose baseline provenance is not documented, while the statistical analysis covers only one baseline; the claim is therefore not yet established at the level promised by the abstract.
major comments (4)
- [Section 4, Experimental Settings, and Table 1] The fairness of the comparison is not established. The text only states that the look-back window T=96 and the prediction lengths F are matched; it does not say whether the eleven baseline entries in Table 1 were re-run by the authors under identical normalization, train/validation/test splits, training epochs, and seeds, or whether the numbers were taken from previous publications. Because several margins in Table 1 are below 0.005 (e.g., ETTh2 horizon 96 MSE: TimeKAN 0.290 vs. TimeMixer 0.289; Weather horizon 336 MSE: 0.263 vs. 0.263), small protocol differences can change the ranking. Please either re-run all baselines under the same protocol or give the source of each baseline number and document why the protocols are equivalent; without this, the first-place counts in Table 1 do not support the state-of-the-art claim.
- [Section 4.1 and Appendix A.4] The state-of-the-art claim is stronger than the evidence in the main experimental setting. The main text concedes that iTransformer wins on Electricity at T=96, and Appendix A.4 states that TimeKAN "performs significantly worse than TimeMixer when T=96" on Electricity, becoming best only after increasing the look-back to 512. The abstract and conclusion should either be qualified to "state-of-the-art at T=96 except Electricity" or the T=512 evidence for Electricity should be integrated into the main comparison; as written, the central claim is not supported by the main experimental setting.
- [Appendix A.3, Table 7] The statistical support is limited to a single comparison. Error bars and confidence levels are reported only for TimeKAN versus TimeMixer on five datasets; no comparison against iTransformer, PatchTST, or the other baselines is provided, and the test procedure is not described. Moreover, Table 7 shows a tie on ETTm2 MSE (0.278±0.001 for both models), so even the "second-best" superiority is not universal. To support the headline claim, the authors should provide error bars for the full Table 1 or at least for the top baselines, and specify the statistical test used.
- [Section 3.3, Eqs. (3)-(4)] The description of the frequency decomposition is not technically accurate as written. The moving-average operation in Eq. (1) is a low-pass filter followed by decimation; it does not remove a single "i-th frequency component", and the FFT zero-padding in Eq. (3) can only reconstruct the bandlimited interpolation of the decimated signal, not the missing high-frequency content of x_i. The residual f_i therefore contains aliasing as well as the intended band. Please either state explicitly that the bands are approximate and explain why the residual is still a useful learned representation, or add a spectral analysis supporting the claim that the decomposition isolates frequency bands.
minor comments (7)
- [Table 3] In the ETTm1 row for "Fixed High-order KANs", the reported MAE 0.269 is inconsistent with the other entries in that row (which are around 0.36-0.37) and is likely a typo; please correct it.
- [Section 4.2 heading] "Varing Look-back Window" should be "Varying Look-back Window".
- [Section 4.3] "TimeMier" should be "TimeMixer".
- [Section 3.5] "we simply need to to supplement" contains a duplicated "to".
- [Table 1] The "1stCount" row is not self-explanatory as rendered; please define how ties are handled and whether the count is over MSE, MAE, or both.
- [Section 4, Experimental Settings] The values of the hyperparameters used in the main experiments (k, d, D, b, L, kernel size, learning rate, batch size, epochs) are not reported; please add a table or explicitly state that they are provided in the released code.
- [Section 2.2 and Table 1] FITS and SparseTSF are discussed as relevant lightweight approaches but are not included in the main comparison; given the paper's efficiency claim, a sentence justifying their omission would be helpful.
Circularity Check
No circularity found; TimeKAN's derivation is self-contained and its SOTA claim rests on external benchmarks rather than on a self-referential reduction.
full rationale
TimeKAN's derivation chain is self-contained. The hierarchical preprocessing (Eq. 1) uses moving-average pooling to build multi-scale sequences; the Cascaded Frequency Decomposition (Eq. 3) uses FFT/IFFT with zero-padding to upsample, and Eq. 4 defines each frequency band as the residual between adjacent scales. Eq. 11 recombines bands by adding the residual back to the upsampled lower-level component, which is the algebraic inverse of the decomposition by construction, not a hidden fit. The forecast output (Eq. 12) is a linear map of the learned representation, trained with L2 loss on standard train/test splits. No model parameter is fitted to the quantity later called a prediction, and no load-bearing claim is justified by a self-citation: the cited KAN, ChebyshevKAN, and baseline results are all independent prior work. Concerns about whether baseline numbers in Table 1 were re-run under identical protocols concern experimental comparability, not circularity, and therefore do not affect the circularity score.
Assumptions & free parameters
free parameters (7)
- Number of frequency bands k =
3 or 4, selected via ablation on each dataset (Appendix A.5, Table 9)
- Moving average window d =
Not reported in the paper
- Embedding dimension D =
Not reported in the paper
- Chebyshev polynomial base order b =
Not reported; ablation uses order 2 (low) and 5 (high)
- Number of Decomposition-Learning-Mixing blocks L =
Not reported in the paper
- Depthwise convolution kernel size =
Not reported in the paper
- Training hyperparameters (learning rate, batch size, epochs, optimizer) =
Not reported in the paper
assumptions (5)
- standard math Kolmogorov-Arnold representation theorem and the approximation power of ChebyshevKAN
- standard math FFT/IFFT with zero-padding preserves the frequency content of the downsampled sequence
- domain assumption Moving average with stride d separates the series into distinct frequency bands
- domain assumption Higher-frequency components require higher-order polynomial basis functions
- ad hoc to paper Reported baseline numbers are comparable to TimeKAN's numbers (same splits, normalization, and evaluation protocol)
Cite this review
Pith. "Pith review of TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting." pith.science (2026). https://pith.science/paper/Z3RPMDPQ
@misc{pith2026250206910,
author = {Pith},
title = {Pith review of: TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting},
year = {2026},
howpublished = {\url{https://pith.science/paper/Z3RPMDPQ}},
note = {Machine review of arXiv:2502.06910}
}
read the original abstract
Real-world time series often have multiple frequency components that are intertwined with each other, making accurate time series forecasting challenging. Decomposing the mixed frequency components into multiple single frequency components is a natural choice. However, the information density of patterns varies across different frequencies, and employing a uniform modeling approach for different frequency components can lead to inaccurate characterization. To address this challenges, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose a KAN-based Frequency Decomposition Learning architecture (TimeKAN) to address the complex forecasting challenges caused by multiple frequency mixtures. Specifically, TimeKAN mainly consists of three components: Cascaded Frequency Decomposition (CFD) blocks, Multi-order KAN Representation Learning (M-KAN) blocks and Frequency Mixing blocks. CFD blocks adopt a bottom-up cascading approach to obtain series representations for each frequency band. Benefiting from the high flexibility of KAN, we design a novel M-KAN block to learn and represent specific temporal patterns within each frequency band. Finally, Frequency Mixing blocks is used to recombine the frequency bands into the original format. Extensive experimental results across multiple real-world time series datasets demonstrate that TimeKAN achieves state-of-the-art performance as an extremely lightweight architecture. Code is available at https://github.com/huangst21/TimeKAN.
Figures
Forward citations
Cited by 6 Pith papers
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Dual-Prototype Disentanglement: A Context-Aware Enhancement Framework for Time Series Forecasting
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MetaKANs generates each KAN activation function from a shared prompt-conditioned meta-learner, cutting trainable parameters toward MLP level while retaining comparable or better accuracy on tested benchmarks.
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Complementary Matrix Gating gives QKAN fast-weight programmers coordinate-wise retain/write control and cuts multi-step quantum-dynamics forecast MSE by at least 91.2% versus scalar gates.
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STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting
STKAN inserts Taylor-polynomial KAN token mixers into spatial and temporal mixing blocks and achieves small but consistent gains over strong baselines on three traffic-flow benchmarks and a tie on a fourth.
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XFMNet: Decoding Cross-Site and Nonstationary Water Patterns via Stepwise Multimodal Fusion for Long-Term Water Quality Forecasting
XFMNet fuses local water-quality time series with remote-sensing precipitation imagery through stepwise multimodal fusion to improve long-term, multi-site water quality forecasting.
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TimeCF: A TimeMixer-Based Model with adaptive Convolution and Sharpness-Aware Minimization Frequency Domain Loss for long-term time seris forecasting
TimeCF, a TimeMixer-based forecaster with adaptive convolutions and a sharpness-aware frequency-domain loss, reports modest MSE/MAE gains over eight baselines on six long-term forecasting datasets.
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The lowest computational cost is highlighted in bold. Datasets ETTH1 ETTH2 ETTm1 ETTm2 Weather Electricity Metric Params MACs Params MACs Params MACs Params MACs Params MACs Params MACs TimeMixer 75.50K 20.37M 75.50K 20.37M 75.50K 20.37M 77.77K 24.18M 104.43K 82.62M106.83K 1.2...
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We infer that its poor performance on the electricity dataset is due to the overly short look-back window (T = 96), which cannot provide sufficient frequency information
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Reviewed August 8, 2026 · model on record in the stance chip above.
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