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REVIEW 5 major objections 5 minor 28 references

Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that KANs classify raw imbalanced tabular data better than MLPs without resampling, but standard imbalance fixes such as SMOTE-Tomek and focal loss actively hurt KANs while helping MLPs reach parity at a fraction of the…

desk verdict A useful but statistically underpowered empirical comparison of KANs versus MLPs on imbalanced tabular data, with the MLP baseline under-specified and the headline claims running ahead of the evidence. read the letter →

arxiv 2507.14121 v1 pith:E3BYVNFH submitted 2025-07-18 cs.LG cs.AI

Pankaj Yadav , Vivek Vijay This is my paper · ORCID
classification cs.LGcs.AI
keywords Kolmogorov-ArnoldNetworksKANclass-imbalancedclassificationtabulardataSMOTE-TomekfocallossB-splineactivationscomputationalcost
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 is trying to establish where Kolmogorov-Arnold Networks (KANs) actually stand on class-imbalanced tabular classification. It claims that KANs naturally handle raw imbalance better than Multi-Layer Perceptrons (MLPs), yet conventional remedies like SMOTE-Tomek resampling and focal loss degrade KANs while only marginally helping MLPs. It further claims that after those remedies are applied, MLPs achieve statistical parity with KANs at far lower computational cost. A sympathetic reader would care because this would mark KANs as a specialized, compute-hungry tool for raw skewed data rather than a general replacement for MLPs.

What carries the argument

The load-bearing mechanism is the replacement of linear weights by learnable univariate functions parameterized as residual B-splines: φ(x) = w_b · silu(x) + w_s · spline(x), grounded in the Kolmogorov-Arnold representation theorem that any multivariate continuous function is a finite composition of univariate continuous functions. This gives each neuron a local, adaptive response shape, which the authors argue lets KANs carve complex decision boundaries on skewed raw data without resampling. Standard imbalance remedies instead disrupt this structure: resampling changes the empirical distribution the splines fit, and focal loss re-weights gradients in a way that apparently derails the univariate optimization. The paper's hypothesis is that these conventional techniques conflict with the mathematical assumptions underlying the Kolmogorov-Arnold decomposition.

What would settle it

A tuning-matched replication using identical hyperparameter search budgets, seeds, and trial counts for both architectures would falsify the inherent-advantage claim if MLPs then match KAN G-mean on raw data within Cohen's d below 0.2.

Watch

Extended reading notes

Core claim

Across ten imbalanced tabular datasets with imbalance ratios from about 1:5 to 1:50, the paper finds that KANs outperform MLPs on raw data (mean balanced accuracy 0.6335 versus 0.5800, G-mean 0.4393 versus 0.2848) without any resampling. The same advantage disappears when standard imbalance remedies are applied: SMOTE-Tomek resampling and focal loss significantly degrade KANs' minority-sensitive metrics (G-mean drops 32 percent under resampling and 39 percent under focal loss; F1 drops 22 to 26 percent) while only marginally benefiting MLPs. After resampling, the two architectures become statistically equivalent (|d| < 0.08 across metrics), but KANs remain roughly three orders of magnitude slower and several times more memory-hungry. The paper concludes that KANs are a specialized solution for raw imbalanced data when compute is unconstrained, not a drop-in replacement for MLPs with imbalance techniques.

Load-bearing premise

The central comparison assumes both network types received equally careful tuning; the paper reports KAN hyperparameters but gives no MLP architecture, training schedule, or search budget, so the raw-data gap might partly be a tuning gap.

Editorial extensions

If this is right

  • On raw imbalanced data, KANs deliver substantially higher minority-sensitive metrics than MLPs, with G-mean and F1 roughly 54 percent and 55 percent higher in relative terms.
  • Applying SMOTE-Tomek or focal loss to KANs degrades their G-mean by 32 to 39 percent and F1 by 22 to 26 percent, while the same techniques only marginally improve MLPs.
  • After resampling, KANs and MLPs are statistically indistinguishable (|d| < 0.08 across all metrics), but KANs still require about 900 to 1,000 times longer training time and more memory.
  • For practice, this means KANs are only worth their cost when raw imbalance is severe, preprocessing is undesirable, and compute is unconstrained; on that view MLPs with imbalance techniques remain the efficient default.
  • A direct research priority follows from the paper's own findings: KAN-specific architectural modifications for imbalance learning, rather than standard data-level or loss-level fixes.

Reading between the lines

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

  • The paper leaves implicit that its degradation result could be tested mechanically: if one compares KAN spline knot distributions before and after SMOTE-Tomek, the hypothesis that resampling distorts local univariate learning becomes directly observable.
  • A way to extend the work would be hybrid pipelines, such as keeping KAN features for representation but using an MLP head with focal loss, which might preserve KAN's raw-imbalance advantage while gaining a compatible loss-based remedy.
  • Because the entire study runs on CPU, the resource conclusions may not transfer to GPU-trained KANs; a GPU replication could narrow or widen the reported cost gap and is a natural next check.
  • The paper's theoretical reconciliation suggestion could be tested on synthetic data with a known sum-of-univariate ground truth, isolating whether resampling breaks the Kolmogorov-Arnold decomposition or merely shifts the optimization landscape.
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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

5 major / 5 minor

Summary. The paper presents an empirical comparison of Kolmogorov-Arnold Networks (KANs) and Multi-Layer Perceptrons (MLPs) on ten imbalanced tabular datasets from the KEEL repository. Under a raw-imbalance baseline and under two imbalance-handling strategies (SMOTE-Tomek resampling and focal loss), the authors report four minority-sensitive metrics, resource measurements, and Wilcoxon-based statistical tests. The central claims are that KANs intrinsically outperform MLPs on raw imbalanced data, that conventional imbalance strategies degrade KAN performance, that KANs incur severe computational costs, and that MLPs with imbalance techniques reach statistical equivalence with KANs. The paper concludes that KANs are a specialized solution for raw imbalanced data under unconstrained compute, rather than a drop-in replacement.

Significance. If established, the claim that KANs inherently handle raw class imbalance better than MLPs, and that resampling and focal loss conflict with KAN structure, would be a notable empirical result for the growing KAN literature. The paper has several strengths: it uses ten standard KEEL datasets, evaluates four imbalance-sensitive metrics, reports optimized KAN hyperparameters in Table 3, includes training-time and memory measurements, and attempts formal statistical validation with Wilcoxon tests. However, the significance is substantially weakened by the absence of any reported MLP configuration or tuning effort, by non-significant p-values for the headline baseline advantage, by an incomplete effect-size table that does not support the abstract's 'across metrics' claim, and by an under-specified experimental protocol. The study is a useful preliminary exploration, but the evidence as reported does not yet support the strong architectural-conflict and inherent-superiority conclusions.

major comments (5)
  1. [§4.1, §5, Table 3] The central baseline claim that KANs inherently outperform MLPs on raw imbalanced data (G-mean 0.4393 vs. 0.2848; F1 +55%) is not verifiable as reported because Table 3 gives KAN hyperparameters but the manuscript never states the MLP architecture, optimizer, learning-rate schedule, regularization, early-stopping rule, or tuning budget. An advantage measured against an unspecified, possibly undertuned baseline cannot support an 'inherent' superiority claim, and because all subsequent degradation claims are expressed relative to this baseline, the omission affects the whole narrative. Please report full MLP configuration details and tuning effort, or rerun the comparison with matched budgets.
  2. [§5, Table 4] The headline statistical evidence is weaker than the text suggests: baseline KAN-vs-MLP differences are non-significant at the 0.05 level (G-mean p=0.06, F1 p=0.10), no per-dataset variance or confidence intervals are reported, and no multiple-comparison correction is applied across the four metrics and several comparisons. In addition, the text reports the training-time Wilcoxon p-value as 0.002 while Table 4 gives p=0.042 for the same comparison, and the claimed memory comparison (p=0.002, d=2.17) is absent from Table 4. Please correct the inconsistencies and present per-metric distributions or confidence intervals.
  3. [§4.2, §5, Table 4] The claim that resampling and focal loss 'fundamentally conflict' with KAN structure rests on a single significant metric out of four: focal-loss G-mean degradation p=0.042, resampled G-mean p=0.057 (not significant at 0.05), and F1 decline of 22-26% reported without a p-value. This does not support the wording 'statistically unambiguous' and is not sufficient for a 'fundamental conflict' conclusion; please report all metric-wise tests and interpret the positive result with appropriate caution.
  4. [Abstract; §5, Table 4] The abstract claims that MLPs with imbalance techniques achieve equivalence with KANs with |d|<0.08 across metrics, but Table 4 reports |d|=0.08 only for balanced accuracy in the resampled comparison; no effect sizes for the other metrics or for the focal-loss comparison are shown. Either provide the complete effect-size table or amend the abstract to state which metric this claim covers.
  5. [§3, §4] The manuscript does not describe the evaluation protocol: number of runs per configuration, random seeds, train/validation/test splits, cross-validation folds, early stopping criteria, or whether metrics are computed on held-out test data. Without this information the aggregated means, p-values, and runtime measurements (e.g., 505s vs. 0.5s) cannot be reproduced or properly interpreted. Please add the full experimental protocol.
minor comments (5)
  1. [Throughout] Typographical errors such as 'o ffer', 'univariarte', 'hormonizes', 'e fficent', and 'Bezier'/'Bezire' should be corrected.
  2. [§2.3] The equation defining spline(x) is incomplete: 'spline(x) = PG+k i=1' has no summand; the B-spline approximation should be written out explicitly.
  3. [§2.2] The support statement 'supp(Bm,p) = [τm+p−1−τm]' appears to be missing the interval endpoints and should be corrected to the standard local-support property.
  4. [§4.2/§5] Section 4.2 states that resampling induces the most severe performance erosion, while Section 5 reports that only focal loss reaches p<0.05; these statements should be reconciled.
  5. [References] Several references are formatted inconsistently (e.g., all-caps author name in [15]) or incompletely (e.g., [12], [17]); full bibliographic details should be provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the paper reports an empirical benchmark comparison, and its central claims rest on measured performance differences rather than on any fitted parameter or self-citational definitional chain.

full rationale

This is an empirical study comparing fixed KAN and MLP architectures on standard KEEL datasets, so there is no derivation chain in which an output is equivalent to an input by construction. The paper's central claim that KANs perform better on raw imbalanced data is supported by reported metric averages (G-mean 0.4393 vs 0.2848; F1 improvement of 55%) and by Wilcoxon/Cohen's d statistics. Those are measurements, not predictions forced by fitted parameters. The only self-citation is reference [22], Yadav, Vijay, and Sihag on synthetic oversampling, cited in Section 3.2 as context for choosing SMOTE-Tomek ('It is also well-established resampling foundations for novel model evaluation'). That citation is background and does not determine the KAN-versus-MLP comparison, the degradation effects, or the computational-cost findings. The claims that resampling and focal loss 'fundamentally conflict' with KANs are empirical observations plus a stated hypothesis in Section 6 ('We hypothesize that data augmentation disrupts the Kolmogorov Arnold representation theorem's assumptions'), not results derived from the theorem itself. The paper does not rename a known result, invoke a uniqueness theorem from the authors' prior work, or smuggle an ansatz in via self-citation. Concerns about MLP hyperparameter tuning parity, which the skeptic raised, are about experimental fairness and reproducibility rather than circularity; even if the MLP baseline were undertuned, that would be a correctness risk, not a case of the paper predicting its own inputs. Therefore the circularity score is 0.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central claims rest on empirical comparisons rather than derivation, but the conclusions depend on several unreported hyperparameter choices and on the way multiclass datasets are converted to binary tasks. The KAN hyperparameters are listed in Table 3; the MLP and loss-function parameters are not.

free parameters (4)
  • KAN hyperparameters per dataset = See Table 3; e.g., yeast4 uses 1 layer, width 7, k=3, grid=5, lr=0.00066.
    Chosen via tuning for each dataset; these choices affect the reported metrics and computational cost.
  • MLP hyperparameters (unreported) = Not stated
    The paper gives no MLP architecture or tuning protocol, so the comparison may not be controlled.
  • Focal loss alpha and gamma = Not stated
    Focal loss in Section 3.2 requires alpha and gamma, but their values are not reported.
  • SMOTE-Tomek parameters = Not stated
    Neighborhood size, sampling strategy, and Tomek link settings are unspecified.
assumptions (3)
  • standard math Kolmogorov-Arnold representation theorem
    Background used in Section 2.1 to justify the KAN architecture; not in dispute.
  • domain assumption One-vs-all binarization preserves the imbalance problem
    Section 3 merges all non-minority classes into one majority for multiclass datasets; the resulting binary tasks may not reflect the original multi-class imbalance.
  • domain assumption CPU-only training and a maximum imbalance ratio of 1:50 are sufficient to characterize KAN behavior
    Section 3.1 limits datasets due to CPU constraints; extreme imbalance or GPU training could change the conclusions.

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Cite this review

Pith. "Pith review of Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective." pith.science (2026). https://pith.science/paper/E3BYVNFH

@misc{pith2026250714121,
  author       = {Pith},
  title        = {Pith review of: Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E3BYVNFH}},
  note         = {Machine review of arXiv:2507.14121}
}
read the original abstract

Kolmogorov Arnold Networks (KANs) are recent architectural advancement in neural computation that offer a mathematically grounded alternative to standard neural networks. This study presents an empirical evaluation of KANs in context of class imbalanced classification, using ten benchmark datasets. We observe that KANs can inherently perform well on raw imbalanced data more effectively than Multi-Layer Perceptrons (MLPs) without any resampling strategy. However, conventional imbalance strategies fundamentally conflict with KANs mathematical structure as resampling and focal loss implementations significantly degrade KANs performance, while marginally benefiting MLPs. Crucially, KANs suffer from prohibitive computational costs without proportional performance gains. Statistical validation confirms that MLPs with imbalance techniques achieve equivalence with KANs (|d| < 0.08 across metrics) at minimal resource costs. These findings reveal that KANs represent a specialized solution for raw imbalanced data where resources permit. But their severe performance-resource tradeoffs and incompatibility with standard resampling techniques currently limits practical deployment. We identify critical research priorities as developing KAN specific architectural modifications for imbalance learning, optimizing computational efficiency, and theoretical reconciling their conflict with data augmentation. This work establishes foundational insights for next generation KAN architectures in imbalanced classification scenarios.

Figures

Figures reproduced from arXiv: 2507.14121 by the authors.

Figure 1
Figure 1. Methodology 3.2. Imbalance Analysis and Strategies We employ both data-level and algorithmic-level strategies to analyze KAN model’s handling of class imbalance. For data￾level, we utilize the SMOTE-Tomek hybrid resampling tech￾nique due to its dual capacity to address both boundary noise and class overlap through combined oversampling and under￾sampling [22]. This approach is particularly relevant for KANs given th… view at source ↗
Figure 2
Figure 2. 4.3. KANs Accuracy vs Computational Performance The resource performance analysis exposes a steep com￾putational penalty for KANs accuracy advantages. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Reference graph

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