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REVIEW 4 major objections 7 minor 1 cited by

KANs for Computer Vision: An Experimental Study

T0 review · 4 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

Pith's one-line read Kolmogorov-Arnold Networks match MLP accuracy on small image benchmarks but need far more parameters.

desk verdict A useful but under-scoped KAN benchmark whose headline parameter-cost claim is contradicted by its own Table 2; worth a referee after the claims are narrowed and experimentation is tightened. read the letter →

arxiv 2411.18224 v2 pith:MTIGWH3A submitted 2024-11-27 cs.CV

classification cs.CV
keywords Kolmogorov-ArnoldNetworksimageclassificationMLPcomparisonB-splineactivationshyperparametersensitivityConvolutionalKANEfficientparameterefficiency
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

Kolmogorov-Arnold Networks (KANs), which replace fixed neuron activations with learnable B-spline functions on connections, have shown promise in symbolic regression but remain untested on large-scale vision. This paper runs a systematic comparison on MNIST, CIFAR-10, and Fashion-MNIST and finds that standalone KANs deliver accuracy on par with MLPs while using substantially more parameters and requiring extra hyperparameter tuning of grid and order. The same cost disadvantage appears when KAN layers are combined with convolutions. The study concludes that in their current form KANs are not a practical substitute for MLP layers in image classification, and that hybrid architectures such as Convolutional KANs are the more promising direction to explore.

What carries the argument

The central object is the KAN layer, where each connection between neurons is a learnable univariate function, typically a B-spline, instead of a fixed activation at the node. The argument is carried by the parameter-scaling formula $O(N^2 L (G+K))$ for a KAN versus $O(N^2 L)$ for an MLP, and by the extra hyperparameters grid and order that control spline resolution and polynomial degree. These two facts explain both the accuracy parity and the parameter/computation gap observed in the experiments.

What would settle it

Run the same KAN-versus-MLP comparison with parameter-matched model sizes, a grid search over grid and order for every configuration, and at least five random seeds per setting, reporting mean and standard deviation; if KANs then show a clear, reproducible accuracy advantage on any of the three datasets, or if an independent reimplementation of EfficientKAN yields materially different parameter counts, the paper's central negative claim would be refuted.

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Extended reading notes

Core claim

On three standard image classification benchmarks, KANs achieve test accuracy that is only slightly better than or equal to MLPs of the same width and depth, while requiring significantly more parameters because each edge carries a spline parameterized by grid intervals and polynomial order. This holds both when KANs replace MLP layers outright and when KAN-based layers are attached to convolutional feature extractors. The paper further shows that KAN accuracy is sensitive to the grid and order hyperparameters, with the best results in a narrow region around grid 2–3 and low order, and that parameter counts grow linearly with both. The intended conclusion is that, at least on small-scale image classification, the flexibility of learnable activations does not translate into a practical advantage, and that future work should focus on adapting KANs into hybrid convolutional designs.

Load-bearing premise

The comparison rests on the assumptions that the third-party EfficientKAN and Convolutional-KAN implementations faithfully represent the KAN architecture, and that the reported single-run accuracy numbers are stable; if an implementation is buggy or a run is an outlier, the measured gaps would not generalize to KANs as a class.

Editorial extensions

If this is right

  • On MNIST, CIFAR-10, and Fashion-MNIST, KANs and MLPs with identical architectures land within about a point of accuracy, so the learnable activations do not provide a meaningful edge for small-scale image classification.
  • Because KAN parameter counts scale linearly with grid and order, even moderate spline settings multiply the computational cost relative to an MLP of the same width and depth.
  • The extra grid and order hyperparameters add a tuning burden that MLPs do not have, and the best accuracy appears only in a narrow range (grid 2–3, low order).
  • Hybrid designs such as Convolutional KANs can beat a small standard CNN on MNIST, suggesting that integrating KANs with convolutional feature extraction is more promising than using them as standalone layers.

Reading between the lines

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

  • The paper's flattening of images into 1D vectors may stack the deck against KANs, since raw pixels are not the compositional input structure KANs are designed to exploit; testing KANs on convolutional feature maps or other latent representations is the natural follow-up.
  • With no repeated seeds or confidence intervals reported, the sub-1% accuracy gaps between KANs and MLPs could be within run-to-run noise; a re-run with error bars would sharpen or weaken the equivalence claim.
  • The parameter-count comparison uses small custom CNNs; a check against modern, well-tuned baselines (such as residual networks) at matched compute would show whether the hybrid advantage survives outside this narrow setting.
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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 / 7 minor

Summary. This paper presents an experimental comparison of Kolmogorov-Arnold Networks (KANs) against MLPs and hybrid KAN/CNN variants on MNIST, CIFAR-10, and Fashion-MNIST. The authors report that standalone KANs achieve accuracy comparable to MLPs but with substantially higher parameter counts, and that KANs are more sensitive to the grid and order hyperparameters. They also experiment with EfficientKAN and Convolutional KAN hybrids, concluding that KANs are not yet a strong alternative for image classification but may be promising in combination with other architectures.

Significance. If the findings were robust, the paper would provide a useful cautionary benchmark for the KAN community, and the parameter-scaling argument O(N^2 L(G+K)) versus O(N^2 L) in Section 3.4.1 is a correct and relevant observation. The heatmap analysis of grid/order sensitivity in Section 3.3 is a helpful visualization that supports the hyperparameter sensitivity claim. However, the paper's central conclusion is broader than its evidence: the hybrid KAN/CNN results in Table 2 contradict the blanket 'higher parameter count' claim for hybrids, and the absence of error bars, repeated runs, or a validation-based model selection weakens the accuracy comparisons. With targeted revisions, the paper could serve as a reference point for practitioners, but in its current form the headline claims are only partially supported.

major comments (4)
  1. [Abstract/Introduction/Conclusion vs. Section 3.4.2, Table 2] The paper's central claim that KANs 'suffer from a significantly higher number of parameters, both when applied alone or combined with other architectures like CNNs' is contradicted by Table 2 in Section 3.4.2. The row 'Convolutional KAN with 1 layer MLP' reports 7.4k parameters and 98.53% accuracy, whereas 'Standard CNN (Small)' has 34k parameters and 97.9% accuracy and 'Standard CNN (Medium)' has 157k parameters and 99.10% accuracy; the hybrid thus uses 4.6x and 21x fewer parameters than the two CNN baselines while matching or nearly matching their accuracy. Moreover, the text above Table 2 states that Convolutional KANs 'achieve higher accuracy compared to standard CNNs,' but the table shows Standard CNN (Medium) is the most accurate model at 99.10%. The hybrid parameter-cost claim needs either to be removed or supported by matched baselines at the same parameter count.
  2. [Sections 3.2 and 3.3] The accuracy comparisons in Figure 3 and Table 1 are based on single runs without error bars or multiple random seeds. Section 3.2 states that the displayed values are 'the best accuracy achieved with these optimizations,' meaning the grid and order were selected on the test set via the sweep in Section 3.3, which risks overfitting to the test set and exaggerating the reported accuracy differences. Without variance estimates or a validation split, the conclusion that KANs achieve 'slightly better or equivalent performance compared to MLPs' is not statistically supported.
  3. [Sections 3.2 and 3.4.1] The experimental protocol is under-specified. Section 3.2 reports a fixed learning rate of 0.05 for all experiments, while Section 3.4.1 states the EfficientKAN experiments used a constant learning rate of 0.01 for 10 epochs; the number of epochs, optimizer, batch size, weight initialization, and hardware are not given for the other experiments, and no code is released. This makes the results difficult to reproduce and leaves open the possibility that differences in training budgets, not architectural properties, drive the observed accuracy gaps.
  4. [Section 3.3] The definition of 'order' in Section 3.3 is internally inconsistent with Section 2.2: Section 2.2 correctly defines order as the polynomial degree of the B-spline segments, but Section 3.3 says 'Order: Denotes the depth of the network, corresponding to the number of layers composing these univariate functions.' This misdefinition obscures the heatmap analysis in Figure 4, where order is varied as a hyperparameter, and should be corrected.
minor comments (7)
  1. [Abstract] The phrase 'specific neural work like Multi-Layer Perceptrons' should be 'specific neural networks such as Multi-Layer Perceptrons.'
  2. [Table 1] The caption says 'Comparison of EfficientKAN and MLP architectures for image classification on the MNIST and CIFAR-10 datasets,' but the table only contains MNIST results; either add the CIFAR-10 column or correct the caption.
  3. [Section 3.4.1] The parameter count formula uses K for grid in 'O(N^2 L(G + K))' while Section 3.4.2 uses K for the convolution kernel; use a consistent symbol (e.g., G for grid and k for spline order) to avoid confusion.
  4. [Section 3.4.2] The illustrated outputs of standard and KAN convolution are hard to follow and appear to show element-wise multiplication rather than a sliding-window convolution; rewriting with standard tensor notation would improve clarity.
  5. [References] References [5] and [29] are identical (Krizhevsky et al., 2012), reference [22] duplicates reference [2], and reference [20] contains an embedded duplicate citation to Fashion-MNIST.
  6. [Section 2.3] The statement that KANs 'offer parameter efficiency by replacing large weight matrices with smaller, learnable univariate functions' is at odds with the paper's own empirical finding of significantly higher parameter counts; the paper should clarify that this is a theoretical advantage that does not materialize in the tested settings.
  7. [Conclusion] The conclusion claims 'excessive computational overhead' but the paper reports no runtime or memory measurements beyond parameter counts; computational cost and parameter count are not equivalent, so this statement should be qualified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the study is an empirical benchmark whose conclusions are drawn from external datasets and third-party implementations, not from any self-referential derivation.

full rationale

The paper's central claims are empirical observations drawn from experiments on MNIST, CIFAR-10, and Fashion-MNIST, comparing KAN variants against MLP and CNN baselines. There is no equation in which a reported prediction is algebraically identical to a fitted input, no fitted parameter is renamed as a prediction, no uniqueness theorem is invoked, and the authors do not rely on their own prior work as load-bearing evidence. The KAN implementations used, EfficientKAN [21] and Convolutional KAN [24], are external public implementations, so any implementation flaws would affect the validity or generalizability of the measurements but would not make the argument circular. The sensitivity analysis in Section 3.3 is likewise a direct measurement of accuracy and parameter count under varied grid and order settings, not a derivation from assumed conclusions. The only notable defect is an internal inconsistency: Section 3.4.2 states that Convolutional KANs 'can achieve higher accuracy compared to standard CNNs,' while Table 2 lists Standard CNN (Medium) at 99.10% as the highest accuracy. That is a correctness and interpretation error, not a circularity. Similarly, the claim that KANs are more sensitive to hyperparameters than MLPs is not supported by a matched MLP hyperparameter sweep, but that is an evidentiary weakness, not a self-referential argument. Accordingly, no circular step is identified and the circularity score is 0.

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

The paper introduces no new entities. It evaluates existing KAN variants and relies on external implementations, standard datasets, and standard training assumptions. The main unstated inputs are the hyperparameters selected per model and the unspecified training protocol.

free parameters (4)
  • Grid size (G) for reported best-accuracy KAN models = Not reported numerically (heatmaps only)
    The accuracies in Figure 3 and Table 1 are the best results from sweeping grid and order, selected on the test set, so the reported comparisons depend on these unstated values.
  • Spline order (k) for reported best-accuracy KAN models = Not reported numerically (heatmaps only)
    The order is tuned per architecture and dataset and not listed in the text, yet it directly determines KAN parameter counts and accuracy outcomes.
  • Learning rate = 0.05
    Fixed across all experiments and chosen by hand; if KANs and MLPs have different optimal learning rates, the accuracy comparison is biased by this un-tuned hyperparameter.
  • Training epochs and optimizer = Not reported for main experiments
    The number of epochs, batch size, and optimizer are unspecified for the Figure 3 and Table 2 experiments, so the accuracy and parameter-comparison results depend on unstated training choices.
assumptions (3)
  • standard math Kolmogorov-Arnold representation theorem justifies the KAN architecture
    Invoked in Section 2 as the theoretical basis for KANs; a standard theorem, not a contribution of this paper.
  • domain assumption Third-party KAN implementations (EfficientKAN and Convolutional KAN) are correct and faithful
    Sections 3.4.1 and 3.4.2 rely on the EfficientKAN GitHub implementation and reference [24]; any implementation error would affect all KAN results.
  • domain assumption Single-run training without seeds or validation splits is representative
    No random seeds, repeats, or confidence intervals are reported, so the accuracy numbers are assumed to be stable point estimates.

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Cite this review

Pith. "Pith review of KANs for Computer Vision: An Experimental Study." pith.science (2026). https://pith.science/paper/MTIGWH3A

@misc{pith2026241118224,
  author       = {Pith},
  title        = {Pith review of: KANs for Computer Vision: An Experimental Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MTIGWH3A}},
  note         = {Machine review of arXiv:2411.18224}
}
read the original abstract

This paper presents an experimental study of Kolmogorov-Arnold Networks (KANs) applied to computer vision tasks, particularly image classification. KANs introduce learnable activation functions on edges, offering flexible non-linear transformations compared to traditional pre-fixed activation functions with specific neural work like Multi-Layer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs). While KANs have shown promise mostly in simplified or small-scale datasets, their effectiveness for more complex real-world tasks such as computer vision tasks remains less explored. To fill this gap, this experimental study aims to provide extended observations and insights into the strengths and limitations of KANs. We reveal that although KANs can perform well in specific vision tasks, they face significant challenges, including increased hyperparameter sensitivity and higher computational costs. These limitations suggest that KANs require architectural adaptations, such as integration with other architectures, to be practical for large-scale vision problems. This study focuses on empirical findings rather than proposing new methods, aiming to inform future research on optimizing KANs, in particular computer vision applications or alike.

Figures

Figures reproduced from arXiv: 2411.18224 by the authors.

Figure 1
Figure 1. Comparison of KAN and MLP architectures in the same model complexity. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Sample images from the MNIST, CIFAR-10, and Fashion-MNIST datasets. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Comparison of KAN and MLP models across various datasets in terms of test accuracy and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Heatmaps showing the impact of grid and order on accuracy and parameter count for two [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification

    cs.CV 2025-01 reject novelty 5.0 of 10

    CKANs are measurably less efficient than standard CNNs, and on ImageNet the accuracy gap is large, but the paper's baseline and timing comparisons are not controlled.

Reference graph

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Reviewed August 12, 2026 · model on record in the stance chip above.