{"id":"8dd2cecb-07ec-4cb3-9c62-63533c83e60c","arxiv_id":"2502.06910","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A frequency-decomposing KAN architecture achieves state-of-the-art or near-state-of-the-art long-term forecasting on five of six datasets with 12-38K parameters.","lead":"TimeKAN is a lightweight neural network for long-term time series forecasting that splits a signal into frequency bands, learns each band with a Kolmogorov-Arnold Network of a matched complexity, and recombines them. On six standard benchmarks it often beats much larger models while using only 12 to 38 thousand parameters.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SOTA claim is load-bearing on baseline comparability; Table 1 does not show that the 11 baselines were re-run under the exact data splits, normalization, and training protocol used for TimeKAN.","rationale":"The reader's weakest assumption is exactly the condition that would invalidate the headline: if the baseline table is not produced under identical conditions, the SOTA claim collapses. I agree with this identification. Additional weaknesses (missing hyperparameters, no error bars for all baselines, Electricity exception) are real but secondary; they would not by themselves overturn the central claim if the comparison were fair. The paper has real strengths: a clear architecture, ablations, and released code, and the lightweight-efficiency numbers are substantial. Therefore the appropriate verdict remains conditional, pending a clean head-to-head comparison.","tokens_in":20,"tokens_out":6027,"duration_ms":116723,"concrete_test":"Run all 11 baselines with their official code under the exact TimeKAN evaluation pipeline: same data files and split ratios (6:2:2 for ETT, 7:1:2 for Weather/Electricity), same normalization (z-score per variable), same T=96 input, prediction lengths {96,192,336,720}, same loss and number of runs, then recompute the 24 MSE/MAE cells of Table 1. If TimeKAN's first-place count drops from 17 to below 10, or if its average MSE margin over TimeMixer falls within the ±0.003 standard deviation reported in Appendix A.3, the SOTA claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that TimeKAN achieves state-of-the-art accuracy while being extremely lightweight. That claim rests on Table 1. The paper specifies only look-back T=96 and prediction lengths; it does not state whether baseline results were re-computed by the authors or copied from prior papers, and it omits normalization details, train/validation/test splits for each dataset, training epochs, and seeds. Because TimeKAN uses a variate-independent pipeline and its own preprocessing, even small protocol differences can shift MSE/MAE by more than the margins seen in Table 1 (e.g., TimeKAN vs. TimeMixer on ETTm2 and Weather). Appendix A.3 reports statistical confidence only against TimeMixer on five datasets, not against the full baseline set; and on Electricity TimeKAN is not SOTA at T=96, requiring a longer look-back in Appendix A.4 to claim competitiveness. If baseline numbers come from heterogeneous sources, the 17-cell SOTA count loses its meaning.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18064,"tokens_out":14518,"duration_ms":124253,"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":[{"comment":"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":"Section 4, Experimental Settings, and Table 1"},{"comment":"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.","section":"Section 4.1 and Appendix A.4"},{"comment":"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":"Appendix A.3, Table 7"},{"comment":"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.","section":"Section 3.3, Eqs. (3)-(4)"}],"minor_comments":[{"comment":"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":"Table 3"},{"comment":"\"Varing Look-back Window\" should be \"Varying Look-back Window\".","section":"Section 4.2 heading"},{"comment":"\"TimeMier\" should be \"TimeMixer\".","section":"Section 4.3"},{"comment":"\"we simply need to to supplement\" contains a duplicated \"to\".","section":"Section 3.5"},{"comment":"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":"Table 1"},{"comment":"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":"Section 4, Experimental Settings"},{"comment":"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.","section":"Section 2.2 and Table 1"}],"recommendation":"major_revision","confidential_remarks":"The main risk is baseline comparability: the headline SOTA claim rests on Table 1, but the provenance of the baseline numbers is not documented. I would ask for either reruns of the baselines under an identical protocol or a clear statement of sources with a justification of protocol equivalence. The architecture and ablations are otherwise reasonable, and the paper is suitable for revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the architecture is a sensible fusion of known pieces—cascaded moving-average decomposition, FFT residual extraction, Chebyshev KANs with order increasing by frequency band, and depthwise convolution—and the ablations show each piece earns its keep. The multi-order KAN idea is modest but real, and the efficiency numbers (12–38K parameters, MACs in the tens of millions) are credible. Code is released. That is the part worth taking seriously.\n\nThe soft spots are about the headline claim, not the mechanism. Table 1 is presented as full results, but the paper only fixes look-back (T=96) and prediction lengths. It never says whether the eleven baselines were re-run under TimeKAN's protocol or copied from earlier papers, and it omits normalization, splits, seeds, and training details. That matters because the margins are thin: on ETTm2 average MSE, TimeKAN ties TimeMixer; on Electricity, iTransformer beats it at T=96, and the paper's Appendix A.4 argues you need a 512 look-back to become competitive—a post-hoc fix that weakens the main-table SOTA claim. Appendix A.3 reports error bars and confidence only against TimeMixer, not the full baseline set, so the '17 SOTA cells' count is not as robust as it looks. The efficiency comparison is fair as far as it goes, but the MACs advantage over TimeMixer is a factor of 2–3, not an order of magnitude; the parameter advantage is the stronger point.\n\nThese are attackable but addressable. The architecture itself is coherent, the ablations are honest, and I don't see any circular reasoning. The paper needs a revised experimental section with explicit baseline sourcing, repeated runs, and a softened claim—'competitive with SOTA while being an order of magnitude smaller' would be accurate.\n\nWho should read it: anyone working on efficient deep time-series models, and people curious whether KANs help outside function fitting. It deserves a serious referee, but the referee should push on the baseline protocol before accepting the SOTA sentence.","headline":"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.","tokens_in":18569,"tokens_out":2631,"would_cite":true,"duration_ms":23288,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T07","62M10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A 12K–38K-parameter network outperforms million-parameter forecasters on five benchmarks.","keywords":["time series forecasting","Kolmogorov-Arnold Network","frequency decomposition","long-term forecasting","lightweight architecture","Chebyshev polynomials","multivariate time series","frequency upsampling"],"falsifier":"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.","tokens_in":17611,"feed_emoji":"📈","tokens_out":8980,"duration_ms":74151,"temperature":0.7,"pith_summary":"The paper tries to show that long-term time series forecasting improves when the series is first split into separate frequency bands and each band is modeled with a representation learner whose capacity matches that band's complexity. The proposed architecture, TimeKAN, uses cascaded frequency decomposition to isolate bands, Multi-order Kolmogorov-Arnold networks (KANs) with increasing polynomial order to learn each band, and frequency mixing to reassemble the series; the whole loop is repeatable. The payoff claimed is empirical: on five of six standard multivariate benchmarks, TimeKAN reports the best average MSE/MAE with only 12,000 to 38,000 parameters, about two orders of magnitude fewer than transformer baselines and far fewer MACs. If the claim holds, accurate long-term forecasting does not require large models, and frequency-aware capacity allocation is a better use of parameters than scaling width or depth. The paper also presents ablations showing that the FFT-based frequency-preserving upsampling, the multi-order KAN design, and depthwise convolution each contribute to the result.","feed_headline":"A 12K-parameter model wins five forecasting benchmarks","feed_subtitle":"TimeKAN splits a series by frequency and learns each band with a KAN, beating models hundreds of times larger.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies Kolmogorov-Arnold Networks, the learnable-univariate-function architecture that TimeKAN adapts for per-frequency representation learning.","marker":"(Liu et al., 2024c)"},{"why":"Provides the Chebyshev-polynomial parameterization of KAN that TimeKAN uses because spline-based KANs are too slow.","marker":"(SS, 2024)"},{"why":"TimeMixer is the strongest MLP baseline and the main second-best; its multi-scale decomposition motivates TimeKAN's frequency-band architecture.","marker":"(Wang et al., 2024a)"},{"why":"PatchTST establishes the variate-independent forecasting strategy that TimeKAN adopts.","marker":"(Nie et al., 2023)"},{"why":"iTransformer is the best baseline on Electricity through cross-variable attention, the comparison TimeKAN must address.","marker":"(Liu et al., 2024b)"},{"why":"DLinear supplies the moving-average trend-season decomposition and the look-back-window scaling argument TimeKAN extends.","marker":"(Zeng et al., 2023)"},{"why":"Autoformer contributes seasonal-trend decomposition and the ETT train/validation/test split used in the experiments.","marker":"(Wu et al., 2021)"}],"fun_headline_variants":["Frequency-decomposed KAN nets achieve top forecasting","12K-parameter TimeKAN beats giants on five benchmarks","Chebyshev KAN layers per frequency band, SOTA results","Lightweight KAN architecture wins time series forecasting","Decompose, learn each band, mix: TimeKAN's recipe"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Frequency-decomposed KAN nets achieve top forecasting","12K-parameter TimeKAN beats giants on five benchmarks","Chebyshev KAN layers per frequency band, SOTA results","Lightweight KAN architecture wins time series forecasting","Decompose, learn each band, mix: TimeKAN's recipe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1508,"prompt_tokens":1072,"completion_tokens":436,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":688,"completion_tokens_details":{"reasoning_tokens":351}},"tokens_in":688,"tokens_out":436,"duration_ms":4130,"temperature":1.0,"reasoning_tokens":351,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T16:37:55.235403+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}