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REVIEW 3 major objections 7 minor 46 references

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

T0 review · 3 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that Convolutional Kolmogorov-Arnold Networks match CNNs on small datasets but fail on ImageNet-1k, with 42.8% Top-1 accuracy versus 56.6% for AlexNet at double the FLOPs and four times the latency.

desk verdict First ImageNet-scale CKAN benchmark with a clean ablation, but the headline accuracy and timing numbers compare against a pretrained baseline and an estimated training time, so the central quantitative claim is not yet supported. read the letter →

arxiv 2501.15757 v3 pith:HJ5FSV3K submitted 2025-01-27 cs.CV cs.AI

Ashim Dahal , Saydul Akbar Murad , Nick Rahimi This is my paper · ORCID
classification cs.CVcs.AI
keywords ConvolutionalKolmogorov-ArnoldNetworksKANImageNet-1kAlexNetLetabularclassificationB-splineefficiencybottleneck
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 tests whether Convolutional Kolmogorov-Arnold Networks (CKANs), which replace learned convolutional kernel weights with trainable B-spline functions, can serve as practical replacements for standard CNNs. On the small-scale MNIST benchmark, a CKAN LeNet matches a CNN's accuracy within 0.1 percentage point but at roughly seven times the FLOPs and more than four times the inference latency. On ImageNet-1k the gap becomes decisive: the authors report 42.8% versus 56.6% Top-1 accuracy for AlexNet-KAN versus AlexNet, with double the FLOPs and four times the latency. On a tabular MoA dataset, the CKAN variant also trails the matched CNN on accuracy, recall, and F1 while training 1.65 times longer. The paper concludes that CKANs are currently compute-heavy specialists best suited to small scientific or tabular tasks, not large-scale vision.

What carries the argument

The central object is the CKAN convolutional layer, which replaces each entry of a CNN kernel with a trainable B-spline function, so the feature map is computed by evaluating splines on pixel windows rather than by multiplying fixed weights. The parameter count grows roughly as the product of input and output dimensions times the number of spline intervals plus polynomial order, making KAN layers about four times heavier per channel than ordinary convolutions; the paper compensates by reducing filter counts in the CKAN variants. The argument runs through three matched model pairs (LeNet, AlexNet, and a 1-D tabular CNN), plus a 24-run ablation sweep on LeNet that varies spline grid size, channel width, ReLU on/off, and 25% structured pruning to isolate which design choice drives the cost.

What would settle it

Train a standard AlexNet from scratch on ImageNet-1k for 100 epochs with the same batch size, optimizer, learning-rate schedule, data pipeline, and GPU hardware used for AlexNet-KAN, and compare Top-1 accuracy and wall-clock training time; if the gap narrows to a few points or the CKAN's 48-day figure is no longer compared with a comparable 100-epoch CNN run, the central efficiency claim would need revision.

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Extended reading notes

Core claim

The paper's central claim is that CKANs are not competitive at ImageNet scale: the spline-based convolutional layer does not capture the hierarchical abstractions required for large-scale visual recognition. In their head-to-head comparison, AlexNet-KAN attains 42.8% Top-1 and 67.8% Top-5 accuracy, while standard AlexNet reaches 56.6% and 79.1%, even though the KAN variant uses roughly double the FLOPs and four times the inference latency. On MNIST the same pattern holds in miniature: accuracy parity within 0.1 percentage point, but a seven-fold FLOP increase and 3.28x per-image latency. The authors attribute the bottleneck to the B-spline activation functions and the absence of low-level spline accelerators, and their 24-run ablation on LeNet identifies spline grid size as the primary cost lever: increasing knots from 4 to 8 yields only +0.19 percentage points while raising FLOPs by 77%.

Load-bearing premise

The headline comparison assumes that using a pretrained AlexNet, together with the historical 'at most 3 days' training-time figure, is a fair proxy for a CNN trained from scratch under the same protocol as the CKAN; if AlexNet were retrained with identical epochs, hardware, and data pipeline, the accuracy and training-time gaps could shrink substantially.

Editorial extensions

If this is right

  • If CKANs cannot beat a 2012 CNN on ImageNet at higher cost, they are not a practical replacement for deep CNNs in large-scale computer vision without further architectural or kernel-level advances.
  • The ablation's Fast-KAN-Lite configuration (4 spline grid, 1.5x width, ReLU on, 25% structured pruning) gives the best accuracy-efficiency trade-off on MNIST and is the recommended default for small-scale tasks.
  • Structured 25% pruning is necessary to make CKANs competitive; it cuts latency by roughly 35% and parameters by 13%, but pruned CKANs remain 1.5-2.0x slower than depth-matched CNNs.
  • Spline grid resolution is the dominant cost lever: grids above 8 knots degrade accuracy while roughly doubling latency, so deployment should keep the grid at 8 or below.
  • The paper reports that its convolutional kernels were implemented without low-level spline accelerators and estimates that kernel-level optimization, quantization, or curriculum grid growth could cut CKAN latency by 30-50%.

Reading between the lines

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

  • Inference: a fairer protocol would compare CKANs against a modern lightweight CNN trained and tuned under the same recipe, which would test whether the gap is specific to spline kernels or to the dated AlexNet backbone.
  • Inference: the reported seven-fold FLOP increase on LeNet suggests that even at small scale CKANs' practical cost is in spline evaluation and memory bandwidth, not parameter count; replacing B-splines with faster basis functions or lookup tables is a testable lever the paper mentions only in future work.
  • Inference: the authors' suggestion that CKANs are better suited to tabular and scientific tasks is not fully established by their MoA result, since the CKAN still lost on accuracy, recall, and F1; additional benchmarks would be needed to support that positioning.
  • Inference: a direct test of the Kolmogorov-Arnold representation theorem's promise, namely interpretability gains from univariate functions, is absent from this paper; whether CKANs offer any scientific interpretability advantage on the MoA dataset remains open.
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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 / 7 minor

Summary. The paper reports an empirical comparison of Convolutional Kolmogorov-Arnold Networks (CKANs) against standard CNN baselines on three tasks: ImageNet-1k with an AlexNet-style CKAN, MNIST with a LeNet-style CKAN, and the MoA tabular dataset with a 1D CNN. The authors report accuracy, precision, recall, F1, FLOPs, inference time, training time, and parameter counts, and add a 24-run ablation on LeNet/MNIST over spline grid size, width multiplier, ReLU use, and pruning ratio. The main conclusion is that CKANs are competitive on small datasets but fail to scale to ImageNet, attaining 42.8% Top-1 accuracy versus 56.6% for AlexNet while taking longer to train and infer.

Significance. If the comparisons were properly controlled, the paper would provide a useful negative result on CKAN scalability and a rare large-scale CKAN training data point. The ablation study is systematic, the code is released, and the authors are transparent about the lack of low-level spline accelerators. However, the central ImageNet claim rests on an uncontrolled baseline: the CNN accuracy comes from a pretrained PyTorch AlexNet, and the CNN training time is a historical hand estimate, not a same-protocol measurement. As a result, the headline 14-16 percentage-point gap cannot currently be attributed to the CKAN architecture.

major comments (3)
  1. [III-A2, IV-D, Table III] The primary evidence for the paper's central claim is the comparison between CKAN and AlexNet on ImageNet. Section III-A2 states that 'We use PyTorch's pretrained AlexNet for CNN's part as it is the industry standard,' which means the 56.6% / 79.1% Top-1 / Top-5 numbers are not produced under the same training protocol as the CKAN model. The pretrained checkpoint was trained with different augmentations, schedule, optimizer settings, batch size, and hardware. A from-scratch AlexNet trained with the CKAN's recipe (100 epochs, batch size 16, 4xK80, normalization only) would likely score lower, potentially narrowing the gap substantially. To support the claim that CKANs 'do not scale gracefully,' the authors must train the CNN baseline from scratch under the identical data pipeline, optimizer, epoch budget, and hardware, and report those numbers.
  2. [IV-A] The claim of a 16x training-time increase ('48 days' vs 'at most 3 days') is not a measured comparison. Section IV-A describes the AlexNet baseline time as 'by hand calculation of the original report,' i.e., a historical estimate from Krizhevsky et al. on 2012-era hardware, whereas the CKAN run was measured on 4x Tesla K80 GPUs with a modern software stack. Different hardware, libraries, and data pipelines make this ratio meaningless as an efficiency comparison. The authors should either measure both models on the same cluster or clearly label the historical number as context and exclude it from the efficiency conclusions.
  3. [Table III, IV-D] The headline ImageNet results are single runs with no error bars or seed repetitions, so the 14-16 pp gap cannot be separated from run-to-run and training-recipe variance. Additionally, the comparison is not parameter-matched: AlexNet KAN has 39,756,776 parameters versus 61,100,840 for AlexNet, so the accuracy gap may partly reflect capacity differences. At minimum, the authors should report mean and standard deviation over multiple seeds and include a matched-parameter or matched-capacity variant of the baseline before attributing the gap to the spline-based representation.
minor comments (7)
  1. [Table III] The FLOPS cell for Tabular CKAN is malformed: '798,61,586' appears to be '79,861,586'; please correct and verify all numeric formatting.
  2. [IV-C] The text reports LeNet-KAN F1 as 97.79 while Table III reports 98.79; these numbers should agree.
  3. [Throughout] The paper uses 'FLOPS' interchangeably for a count of operations; FLOPs (count) and FLOPS (rate) should be distinguished.
  4. [Eq. (7)-(10)] Equation (7) has index errors: the feature-map formula uses 'a_{i-x,i-y}' but the kernel indices are inconsistent with Equations (8)-(9); please rewrite the convolution definition cleanly.
  5. [V.B] The MNIST-based conclusion that 'we therefore set an upper bound of g=8 for any CKAN deployed in resource-constrained environments' is overgeneralized; please qualify this recommendation to the tested setting.
  6. [VI-D] Section VI-D mentions 'ImageNet-100 pilot runs' that are not described anywhere in the results; either document the pilot or remove the reference.
  7. [III-C, Table III] The precision, recall, and F1 definitions for the multi-class ImageNet task do not specify whether macro, micro, or weighted averaging is used; please state the averaging scheme.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity found: the paper's results are measured benchmarks, not derivations that reduce to their own inputs.

full rationale

The paper's central claims—CKAN accuracy, FLOPs, latency, parameter counts, and training time—are measured outcomes from explicit experimental runs. No equation or argument defines one reported quantity in terms of another predicted quantity, and no fitted parameter is later renamed as a prediction. The use of PyTorch's pretrained AlexNet as the CNN baseline (Section III-A2) is a training-recipe asymmetry that affects experimental fairness, but it is not circular: the 56.6%/79.1% baseline numbers are external checkpoint measurements, not values derived from the CKAN results or from the paper's own fitting procedure. Hyperparameter choices such as spline grid size, width multiplier, and pruning ratio in the Section III-D ablation study are standard experimental design; they are tuned to the task and reported transparently, rather than used to manufacture a conclusion equivalent to the tuning itself. The paper contains no load-bearing self-citations and invokes no uniqueness theorem. The ablation study is self-contained, and its conclusions are contingent empirical observations. Accordingly, any concern about the pretrained-versus-from-scratch comparison belongs under correctness risk, not circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rest on several unstated implementation and baseline choices. The spline grid and order for the main runs are not reported, the pretrained AlexNet is used as a baseline, and the training-time comparison is a historical estimate. None of these are new physical entities; they are experimental assumptions.

free parameters (4)
  • Spline grid size G for main experiments = not reported; ablation uses 4, 8, and 16
    The efficiency and accuracy of the CKAN models depend on the grid; the main ImageNet and MNIST runs do not state which grid was used, so the measured gaps may not be representative.
  • Spline polynomial order K = not reported (likely default)
    Parameter count and FLOPs scale with K, but K is never stated in the main comparison.
  • Filter count adjustments for CKAN variants = one-fourth reduction or rounding to match CNN parameter counts
    The authors adjust filter counts to balance parameter numbers (Section III-A2); these choices affect accuracy and speed.
  • Pruning ratio p (ablation) = 0% or 25%
    Structured pruning is a post-hoc optimization; the best configuration Fast-KAN-Lite uses p=25%.
assumptions (5)
  • standard math Kolmogorov-Arnold representation theorem justifies replacing learned activations with B-splines.
    Section II, Eq. (1).
  • domain assumption The B-spline convolution layer from Bodner et al. is correctly implemented in PyTorch for all benchmarks.
    Section II and III; no formal verification or test for implementation correctness is provided.
  • ad hoc to paper The pretrained PyTorch AlexNet is an acceptable stand-in for a CNN trained from scratch under the same data and budget.
    Section III-A2: 'We use PyTorch's pretrained AlexNet for CNN's part as it is the industry standard.' This is load-bearing for the accuracy comparison.
  • ad hoc to paper Historical training time of AlexNet (at most 3 days) is comparable to the measured CKAN training time on modern GPUs.
    Section IV-A: 'by hand calculation of the original report, would have required at max 3 days'.
  • domain assumption FLOPs and MACs measured by THOP reflect the computational cost of both models consistently.
    Section III-D uses THOP; no validation that the B-spline layer's operations are counted on the same basis as standard convolutions.

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Cite this review

Pith. "Pith review of Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification." pith.science (2026). https://pith.science/paper/HJ5FSV3K

@misc{pith2026250115757,
  author       = {Pith},
  title        = {Pith review of: Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HJ5FSV3K}},
  note         = {Machine review of arXiv:2501.15757}
}
read the original abstract

Algorithmic level developments like Convolutional Neural Networks, transformers, attention mechanism, Retrieval Augmented Generation and so on have changed Artificial Intelligence. Recent such development was observed by Kolmogorov-Arnold Networks that suggested to challenge the fundamental concept of a Neural Network, thus change Multilayer Perceptron, and Convolutional Neural Networks. They received a good reception in terms of scientific modeling, yet had some drawbacks in terms of efficiency. In this paper, we train Convolutional Kolmogorov Arnold Networks (CKANs) with the ImageNet-1k dataset with 1.3 million images, MNIST dataset with 60k images and a tabular biological science related MoA dataset and test the promise of CKANs in terms of FLOPS, Inference Time, number of trainable parameters and training time against the accuracy, precision, recall and f-1 score they produce against the standard industry practice on CNN models. We show that the CKANs perform fair yet slower than CNNs in small size dataset like MoA and MNIST but are not nearly comparable as the dataset gets larger and more complex like the ImageNet. The code implementation of this paper can be found on the link: https://github.com/ashimdahal/Study-of-Convolutional-Kolmogorov-Arnold-networks

Figures

Figures reproduced from arXiv: 2501.15757 by the authors.

Figure 1
Figure 1. Summary of Research Methodology results across bigger and diverse dataset (easy to scale) and fast inference (easy to deploy). III. METHODOLOGY Our research procedure is highlighted on the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. 1D CNN architecture [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Imagenet Sample from [43] D. Ablation-Study Protocol The ablation study protocol grid is presented in table II. In order to make the study viable in terms of compute hours, we choose to do the 24-run ablation study in the LeNet architec￾ture. We specifically avoid doing it on AlexNet architecture because (more discussed on section IV), a 24 sweep training run in the ImageNet data would cost us approximately 1150 GPU… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Radar Plot of Performance Metrics of All Tested Models. All metrics except accuracy are inverted after normalization. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Ablation study on Fast-KAN LeNet-5: impact of spline grid size, channel width, ReLU removal, and structured pruning [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.