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REVIEW 3 major objections 4 minor 35 references

Is the Statistical Advantage Worth the Cost? An Empirical Comparison of KANs and MLPs for Structured Data Classification

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read KANs have a significant but medium-sized accuracy edge over MLPs on tabular data, delivered at roughly 16 times the parameter cost.

desk verdict Useful raw benchmark, but the statistical significance claim is arithmetically impossible with n=3 and the test unit is undisclosed — fix the stats or soften the claims. read the letter →

arxiv 2607.13413 v1 pith:2FCAL54Y submitted 2026-07-15 cs.LG cs.AI

Matthew Steven P. Toledo , Justine Raphael H. Jacinto , Vivekjeet Singh Chambal , Rodolfo C. Camaclang III , Jamlech Iram N. Gojo Cruz , Reginald Neil C. Recario This is my paper
classification cs.LGcs.AI
keywords Kolmogorov-Arnoldnetworksmultilayerperceptrontabulardataempiricalbenchmarkingstatisticalsignificanceeffectsizecost-benefitanalysisclassification
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 tries to establish whether Kolmogorov-Arnold Networks are worth adopting over standard MLPs for structured-data classification. Using twelve tabular datasets spanning binary, multiclass, multilabel, and ordinal tasks, both architectures were trained under fixed, untuned configurations and compared on test accuracy, F1-score, paired hypothesis tests, and effect sizes. The paper claims KANs achieve a statistically significant aggregate accuracy advantage over MLPs, strongest in binary and multiclass problems, with no significant difference in multilabel and ordinal tasks. It also shows this advantage comes with roughly 16 times more parameters and substantially higher training and inference time. The practical takeaway the paper argues for is contextual: KANs for precision-critical applications, MLPs when computational resources are limited.

What carries the argument

The central mechanism is the Kolmogorov-Arnold theorem, which states that any continuous multivariate function can be represented as a finite sum of univariate functions. KANs implement this by replacing each scalar connection weight with a learnable B-spline univariate function, shifting expressivity from node activations to edge-based mappings. This is what gives KANs their adaptive, localized nonlinear modeling, and also what drives their parameter complexity to O(N^2 G L) versus MLP's O(N^2 L), where G is the grid size. The cost-benefit analysis in the paper follows directly from this architectural contrast.

What would settle it

Recompute the paired tests from the per-dataset test accuracies in Table 4: for the binary category, the three MLP-minus-KAN differences are approximately -0.048, -0.005, and -0.034, which yield a paired t-test p-value of roughly 0.15, not 0.001, and a two-sided Wilcoxon signed-rank test on three pairs has a minimum possible p-value of 0.25. If the paper's p=0.001 cannot be reproduced under any legitimate unit of analysis, the central significance claim fails.

Watch

Extended reading notes

Core claim

Under standardized, untuned training conditions across twelve tabular datasets, KANs outperform MLPs on test accuracy in 9 of 12 datasets and on F1-score in 10 of 12 datasets. Paired hypothesis testing at alpha = 0.05 reports statistically significant KAN superiority in binary and multiclass categories and in the aggregate, with a medium overall effect size (Cohen's d = -0.46). The authors interpret this as a real but modest architectural advantage, attributable to KAN's learnable spline-based univariate functions, and weigh it against KAN's substantially higher parameter count, training time, and inference latency. They conclude the choice depends on whether accuracy or computational effici

Load-bearing premise

The statistical-significance claim depends entirely on the paired hypothesis tests reported in §4.3, but those tests are reported with p=0.001 for categories that contain only three datasets and with no stated sample size; if those p-values are not valid, the claimed KAN advantage is not established.

Editorial extensions

If this is right

  • If the paper's central claim is correct, KANs are the better default choice for binary and multiclass tabular classification when accuracy is the priority and computational cost is not binding.
  • For multilabel and ordinal tasks, the reported data show no statistically significant difference, so the cost-benefit calculation there favors the cheaper MLP.
  • The medium aggregate effect size implies that switching from an MLP to a KAN yields only a small accuracy gain near the margin, not a transformative jump.
  • KAN's roughly 16x parameter overhead and much higher inference latency make it difficult to justify in low-latency or resource-constrained deployment settings.
  • The paper's findings suggest architectural selection for tabular data should be guided by the operating environment, not by a one-size-fits-all preference.

Reading between the lines

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

  • The reported p-values of 0.001 for categories with only three datasets each are arithmetically suspect: a two-sided paired Wilcoxon test on three pairs cannot reach 0.001, and the reported differences also do not produce such a p-value under a paired t-test. The aggregate significance claim should be read as unverified until the unit of analysis is clarified.
  • Because both models were deliberately left untuned, the comparison measures out-of-the-box behavior. Tuning MLP hyperparameters would likely narrow the gap, potentially flipping the cost-benefit conclusion for many applications.
  • Tree-based models, which are not part of this benchmark, often outperform both architectures on tabular data, so the practical relevance of KAN's advantage over MLP in real-world tabular pipelines may be limited.
  • A natural extension would be to run the same comparison under a properly powered analysis with more datasets per category and honest error bars, which would either confirm or dissolve the claimed aggregate advantage.
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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

3 major / 4 minor

Summary. This manuscript reports an empirical comparison of Kolmogorov-Arnold Networks (KANs) and multi-layer perceptrons (MLPs) on twelve tabular classification datasets spanning binary, multiclass, multilabel, and ordinal tasks. Both architectures are trained under fixed, untuned hyperparameters with standardized preprocessing, and compared on test accuracy and F1-score. The paper reports that KANs achieve higher accuracy on 9/12 datasets and higher F1 on 10/12, with paired tests in Table 5 indicating statistically significant advantages in binary, multiclass, and overall comparisons (p=0.001), alongside a medium aggregate effect size (d=-0.46). A cost–benefit analysis concludes that KANs are preferable when accuracy is paramount, while MLPs remain competitive under computational constraints.

Significance. If the statistical claims were valid, this would be a useful benchmark: it evaluates KANs on a broader set of task types than most prior work, uses publicly available datasets, and reports parameter counts, training times, and inference latency, which is valuable for practitioners. The raw accuracy and F1 tables (Table 4) are internally consistent and the descriptive wins are informative. However, the central scientific contribution — that KANs 'statistically outperform' MLPs — depends entirely on the p-values in Table 5, which are arithmetically incompatible with the reported data. The manuscript does not disclose the test unit, and with three datasets per category the reported p=0.001 is impossible for both a paired t-test and a two-sided Wilcoxon test. The only plausible route to p≈0.001 would be pooling the five repeated runs per dataset, which violates independence because runs on the same dataset share the same test set. As a result, the headline claim is not reproducible from the reported statistics, and the paper's main conclusion is unsupported. The computational-cost comparison and per-dataset descriptive results remain valid but are of secondary interest.

major comments (3)
  1. [§4.3, Table 5] The reported p=0.001 for the Binary, Multiclass, and Overall paired tests cannot be reproduced from the data in Table 4. With only three datasets per category, a two-sided Wilcoxon signed-rank test has a minimum p-value of 0.25, and a paired t-test on the binary differences (MLP−KAN: −0.0480, −0.0045, −0.0336) yields t≈−2.2, df=2, p≈0.15. For the overall comparison with 12 datasets, d=−0.46 gives t≈−1.6, p≈0.13. The only way to obtain p=0.001 is to treat the five repeated runs per dataset as independent observations, but those runs share the same test set and are not independent. The manuscript never states the unit of analysis, so the central claim of statistical significance is not reproducible.
  2. [§4.3, Table 5 (Multiclass row)] The Multiclass row reports a Wilcoxon signed-rank test with p=0.001 and rank-biserial correlation r_rb=−1.00. With n=3 datasets, all three differences favor KAN (Dropout, Yeast, Statlog), which gives the minimum possible two-sided p=0.25, not 0.001. The effect size r_rb=−1.00 is also the maximum possible for n=3. This indicates either an arithmetic error or an undisclosed pooling of non-independent runs. The same issue applies to the binary (paired t, p=0.001) and Overall (paired t, p=0.001) rows.
  3. [Abstract and §5] The abstract and conclusion state that 'KANs statistically outperform MLPs in binary and multiclass domains' and 'achieve a significant aggregate advantage across all datasets.' These claims rest entirely on the invalid p-values in Table 5. The descriptive result — KAN wins on 9/12 accuracy and 10/12 F1 — is not, by itself, evidence of statistical significance. Since the p-values are not reproducible with the stated experimental design, the paper's main empirical claim is unsupported. A revision would need either to correct the statistical analysis (which with only three datasets per category cannot yield the claimed significance) or to substantially reframe the contribution as a descriptive benchmark.
minor comments (4)
  1. [§4.1] Typo: 'therotical complexities' should be 'theoretical complexities'. Also, the claim that the configurations maintain 'equivalent parameter complexity' is contradicted by Table 3, where KAN uses roughly 16× more parameters; the sentence likely means equivalent network width/depth, not parameter count.
  2. [§3.3 / Table 2] For multilabel tasks, MLP uses hidden layers [128,64] while KAN uses [64,32]. This is not an 'equivalent' architecture comparison; the capacity differs independently of the spline parameterization. The authors should justify this asymmetry or adopt the same width/depth for both.
  3. [§5] The limitations paragraph refers to 'multilabel datasets were trained for fewer epochs (i=20)' — 'i' appears to be a typo for the number of epochs; also the paper should state whether the 80/20 split for multilabel tasks is stratified on any label property, since random splitting of multilabel data can affect evaluation.
  4. [§4.3] The test-selection procedure (Anderson–Darling normality test) is applied to groups of size n=3 per category. Such a test has extremely low power at n=3 and cannot reliably distinguish normal from non-normal distributions. This should be acknowledged, and the choice of paired t-test versus Wilcoxon should be justified more carefully.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is an empirical benchmark with no derivation looped into its inputs.

full rationale

The paper claims no first-principles result and makes no prediction from fitted parameters; it is a direct empirical comparison of KANs and MLPs on public datasets. The architecture configurations are explicitly taken from external foundational references (Gorishniy et al. for MLP, Liu et al. for KAN) and fixed before evaluation, so this is not an instance of fitting a parameter and then predicting a closely related quantity. The complexity formulas cited from [22] are external theoretical statements used to explain observed parameter and runtime counts, not looped back into the empirical outcome. There are no self-citations by the paper's authors and no uniqueness theorem imported from same-author work. The acknowledged limitations (fixed hyperparameters, fewer epochs for multilabel tasks) weaken external validity but do not make any result equal to its input by construction. The apparent irreproducibility of the reported p-values in Table 5 is a statistical correctness and reporting concern, not a circularity concern under the provided scoring rules. Accordingly, the appropriate finding is no significant circularity.

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

The paper introduces no new mathematical objects or entities. Its central claims rest on the chosen datasets, fixed hyperparameters from the original papers, and the correctness of the statistical computations. The most consequential unstated premise is that the p-values in Table 5 were computed correctly; the reported effect sizes and sample sizes do not support them.

free parameters (4)
  • MLP hidden widths = [16,16] standard; [128,64] multilabel
    Chosen from Gorishniy et al. (Ref 13). Not fitted to these datasets. The multilabel widths are larger than KAN's, yet MLP still has fewer parameters.
  • KAN hidden widths = [16,16] standard; [64,32] multilabel
    Chosen from Liu et al. (Ref 22). Not fitted. The smaller multilabel width still yields 16x more parameters due to splines.
  • KAN grid size / spline order = Grid 5, k=3 standard; Grid 3, k=2 multilabel
    Fixed hyperparameters from Liu et al. affecting function complexity and compute cost.
  • Learning rate / epochs / batch size = lr=1e-3; 100 epochs standard, 20 multilabel; batch 256
    Fixed across models. The lower epoch count for multilabel may under-train both models, especially KAN, as the authors note in limitations.
assumptions (4)
  • standard math Kolmogorov-Arnold theorem: any continuous multivariate function is a finite sum of univariate functions
    Invoked in Sec. 2 as the theoretical motivation for KAN; not used to derive the benchmark results.
  • domain assumption The 12 datasets are representative of structured tabular classification problems
    The paper generalizes conclusions to tabular data broadly based on 12 datasets, without a sampling framework (Sec. 3.1).
  • domain assumption Complexity formulas O(N^2 G L) and O(2k B N^2 G L) for KAN are correct as cited
    Taken from Liu et al. (Ref 22) and used in Sec. 4.1 to explain the cost difference; not re-derived.
  • domain assumption Paired test assumptions (e.g., normality of differences) are satisfied after Anderson-Darling checks
    The choice of t-test vs Wilcoxon in Sec. 4.3 is justified by normality tests, but the test results are not auditable because no sample sizes or raw differences are given.

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Cite this review

Pith. "Pith review of Is the Statistical Advantage Worth the Cost? An Empirical Comparison of KANs and MLPs for Structured Data Classification." pith.science (2026). https://pith.science/paper/2FCAL54Y

@misc{pith2026260713413,
  author       = {Pith},
  title        = {Pith review of: Is the Statistical Advantage Worth the Cost? An Empirical Comparison of KANs and MLPs for Structured Data Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2FCAL54Y}},
  note         = {Machine review of arXiv:2607.13413}
}
read the original abstract

This study presents an empirical benchmarking comparison between Kolmogorov-Arnold Networks (KANs) and Multi-Layer Perceptrons (MLPs) on structured tabular classification tasks. Motivated by the growing interest in KANs as an alternative function-approximating architecture, we evaluate their out-of-the-box performance on twelve publicly available datasets spanning binary, multiclass, multilabel, and ordinal problems. Both models were trained under standardized preprocessing, architecture, and fixed hyperparameter settings, with performance assessed using test accuracy and F1-Score, paired hypothesis testing, and effect size analysis. Results show that KANs statistically outperform MLPs in binary and multiclass domains and achieve a significant aggregate advantage across all datasets. However, the observed medium effect size (d = -0.46) raises an important cost-benefit consideration: while KANs offer superior generalization through adaptive spline-based mappings, this advantage comes with substantially higher parameter and computational complexity relative to the MLP baseline. These findings suggest KANs are the preferred choice for high-precision applications, while MLPs remain a robust and efficient option for resource-constrained environments. Future work should extend this analysis to additional data modalities to further refine these architectural selection criteria.

Figures

Figures reproduced from arXiv: 2607.13413 by the authors.

Figure 1
Figure 1. From Top to Bottom: Training and validation accuracy of KAN and MLP across dataset categories from Binary (top row), Multiclass (middle row), Multilabel (third row), and Ordinal (bottom row) class tasks [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

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