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REVIEW 3 major objections 5 minor 27 references

ProKAN: Progressive Stacking of Kolmogorov-Arnold Networks for Efficient Liver Segmentation

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read ProKAN claims a Kolmogorov-Arnold network that adds blocks only when validation loss plateaus beats fixed MLP and KAN baselines on liver tumor segmentation, reaching 96.7% validation accuracy and 92.3% Dice.

desk verdict ProKAN's progressive-depth idea is plausible, but the paper's own tables contradict each other, so the empirical claims collapse. read the letter →

arxiv 2412.19713 v1 pith:AMWEBCTX submitted 2024-12-27 eess.IV cs.CVcs.LG

Bhavesh Gyanchandani , Aditya Oza , Abhinav Roy This is my paper · ORCID
classification eess.IVcs.CVcs.LG
keywords Kolmogorov-ArnoldNetworksprogressivestackinglivertumorsegmentationB-splineactivationsoverfittingmitigationLiTS17medicalimagecomputationalefficiency
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 proposes proKAN, a training scheme that grows a Kolmogorov-Arnold Network (KAN) in depth during training instead of fixing the architecture in advance. The growth rule is: when validation loss stops improving while training loss keeps falling, add another KAN block; each addition also enlarges the spline grid, raises the spline degree, lowers the learning rate, and increases regularization. On the LiTS17 liver tumor segmentation benchmark, the authors report 96.7% validation accuracy, a 92.3% Dice score, and 5.5 hours of training, compared with 92.3%, 85.2%, and 4.0 hours for an MLP and 95.1%, 89.5%, and 8.0 hours for a fixed KAN. The paper interprets the smaller train-validation gap across 10-fold cross-validation as evidence that the progressive rule mitigates overfitting. If the numbers hold, proKAN would offer a practical self-sizing alternative to fixed-depth networks for volumetric medical segmentation.

What carries the argument

The load-bearing mechanism is the progressive stacking rule for KAN blocks. A KAN block is a layer in which each connection is a learnable univariate function parameterised by a B-spline, so the network has no fixed activation shapes; the Kolmogorov-Arnold theorem licenses the decomposition of a multivariate function into sums of such univariate functions. proKAN starts with a base MLP augmented by one KAN block and inserts further blocks when the average validation loss over a plateau window is flat while training loss is still falling, or when validation accuracy has begun to decline. Each insertion adjusts the architecture's hyperparameters, with spline grid granularity and degree increasing, learning rate decaying, and regularization strengthening, so that added capacity is paired with stabilisation. The rule is what is supposed to convert KAN flexibility into efficient, overfitting-resistant segmentation.

What would settle it

Run a controlled comparison on LiTS17 where a fixed-depth KAN is trained with standard early stopping and the same total compute as proKAN; if the fixed KAN matches or beats proKAN on validation accuracy, Dice, and wall-clock time, the progressive rule is not responsible for the reported gains. Independently, recompute Dice from proKAN's predicted masks against ground truth, since the value should be near 0.92 if Tables III and IV are right and near 0.58 if Table VI is right.

Watch

Extended reading notes

Core claim

The central claim is that progressive stacking of KAN blocks, starting from a minimal network and adding capacity only when validation plateaus while training loss continues to decrease, produces higher liver segmentation accuracy, better Dice overlap, and shorter training time than both MLPs and fixed KANs. The authors frame this as a general overfitting-mitigation strategy: the network stops growing once the validation signal says further capacity would be wasted, so it avoids both underfitting and unnecessary computation. They attribute the flexibility of the building block to the Kolmogorov-Arnold representation theorem, with each connection carrying a learnable univariate B-spline activation rather than a fixed nonlinearity. In their experiments on LiTS17 CT scans, proKAN reaches 96.7% validation accuracy and a 92.3% Dice score; the authors also report it bests all seven previously published segmentation baselines listed on the same benchmark, with 15.3 ms per-image inference and 2.8 GB GPU memory usage.

Load-bearing premise

The claim collapses if adding KAN blocks when validation loss plateaus while training loss falls does not actually reduce overfitting, and the paper provides no learning curves, ablations, or an early-stopping control to demonstrate that the rule helps rather than hurts.

Editorial extensions

If this is right

  • If the progressive rule works, architecture depth becomes a training-time decision rather than a pre-committed hyperparameter, so the same code can serve small and large datasets without manual depth search.
  • The reported 5.5-hour training time against 8.0 hours for a fixed KAN suggests that a self-sizing KAN can recover most of the accuracy gain of KANs while avoiding their full computational cost.
  • The dynamic hyperparameter schedule, with grid size and spline degree increasing and learning rate decreasing as blocks are added, gives a concrete recipe for scaling KAN capacity that could transfer to other 3D segmentation tasks.
  • If the Dice and accuracy numbers reproduce, proKAN would be competitive with published LiTS liver segmentation methods while offering the interpretability of spline coefficients.

Reading between the lines

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

  • The growth rule is the part most worth testing in isolation: a fixed KAN trained with standard early stopping is the natural control, since adding capacity when validation plateaus runs against the usual expectation that such a moment signals too much capacity, not too little.
  • The paper's two reported Dice values for proKAN, 92.3% in Tables III and IV versus 0.58 in Table VI, cannot both be right; reconciling them would clarify which claim the method actually supports.
  • If progressive stacking is validated, the same plateau-detection criterion could be applied to other architecture families, such as deciding when to unroll more transformer layers or add residual blocks, making it a generic capacity-scheduling rule rather than a KAN-specific trick.
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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 / 5 minor

Summary. The paper introduces proKAN, a progressive stacking method for Kolmogorov-Arnold Networks intended for liver tumor segmentation. The method starts with a small KAN-enhanced MLP and adds KAN blocks during training when validation loss plateaus while training loss continues to decrease, with associated dynamic adjustments to grid size, spline degree, learning rate, and regularization. The authors report experiments on the LiTS17 dataset comparing proKAN against MLPs and fixed KANs, and claim state-of-the-art accuracy, Dice score, and training time, as well as improved interpretability and overfitting mitigation.

Significance. If the reported results were reliable, the idea of dynamically growing a KAN's capacity based on validation behavior would be a useful contribution to efficient medical image segmentation. However, the central quantitative claim is undermined by internal contradictions in the paper's own tables, as detailed below. The paper also provides no learning curves, no ablation of the progressive-stacking rule, no code or reproducibility artifacts, and no comparison against standard early stopping, so the overfitting-mitigation claim is not currently supported. The method itself is not inherently implausible, but the experimental evidence as presented does not justify acceptance.

major comments (3)
  1. [Tables III and VI] The reported Dice scores for proKAN are mutually inconsistent. Table III reports proKAN Dice Score = 92.3% (with MLP 85.2% and KAN 89.5%), while Table VI reports the average Dice score over 10-fold cross-validation as 0.58 for proKAN, 0.57 for KAN, and 0.55 for MLP. Since DSC is defined in Section IV-B as a measure in [0,1], either the Table III values are percentages (0.923) or the Table VI values are decimals (0.58), and the two cannot describe the same model on the same benchmark. This is a mechanical contradiction, not a matter of interpretation; the paper does not provide a coherent quantitative basis for the claim that proKAN outperforms both baselines in Dice score.
  2. [Table IV] In Table IV, proKAN reports mIoU = 78.46 and HD = 3.50, which are exactly identical to the values reported for PVTFormer in the same table, even though the Dice values differ (92.3% vs. 86.78%). Exact equality of two independent evaluation metrics across two different models is not impossible, but it is highly implausible without comment. The paper gives no explanation for this coincidence, and the row therefore raises a serious concern that these metrics were not independently computed for proKAN. This directly affects the state-of-the-art comparison in the abstract and Section IV-C.
  3. [Section III-B and Section IV-D] The central methodological premise is that adding KAN blocks when validation loss plateaus (while training loss continues to decrease) mitigates overfitting. This premise is not supported by any evidence in the paper. No learning curves are shown, no ablation is performed, no comparison with standard early stopping is given, and the 10-fold cross-validation tables only report final accuracy and Dice, not the evolution of the training/validation gap. The paper also uses the validation set both to decide when to add blocks and to report the headline validation accuracy, creating a selection-on-validation effect that is not discussed. These issues are load-bearing because the overfitting-mitigation claim is one of the two main advertised contributions.
minor comments (5)
  1. [Abstract and Section I] The abstract and introduction claim that proKAN is designed for real-time clinical deployment on FPGAs and ASICs, but Section IV-F only reports inference speed and GPU memory usage; no FPGA or ASIC experiments or analyses are presented.
  2. [Section II and Section III] The term 'KAN binding' appears in the introduction and related work, but it is never formally defined or used in the methodology; Section III only describes KAN blocks and progressive stacking.
  3. [Table IV caption] The caption of Table IV cites reference [2] (Hame and Pollari) as the benchmark dataset, but the dataset is LiTS17, and [20] is the actual LiTS benchmark reference; the citation appears to be incorrect.
  4. [Section IV-C] The text says 'Table III summarizes the performance' and claims proKAN mitigates overfitting compared to MLPs and KANs, but Table III only reports validation accuracy, training time, and Dice score; it contains no measure of overfitting such as train-validation gap.
  5. [Section III-C and Table II] The dynamic hyperparameter adjustments (grid size, spline degree, learning rate, regularization) are stated with free parameters ΔG, Δk, α, and Δλ, but no values for these parameters are given anywhere in the paper, making the experiments irreproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported results are empirical, not derived by construction from the stacking rule.

full rationale

The paper does not derive its reported results from its own inputs in a circular manner. The progressive stacking rule (Section III-B) uses validation loss/accuracy trends to decide when to insert KAN blocks, but the reported validation accuracy, Dice score, and training time are empirical measurements, not algebraic consequences of that rule. No fitted parameter is renamed as a prediction; the hyperparameter updates in Section III-C are prespecified schedules rather than fits to the target metrics. The paper cites no prior works by its own authors, so no self-citation chain is load-bearing. The Kolmogorov-Arnold representation theorem and B-spline definitions are standard external mathematics, not asserted uniquely by this paper. The internal inconsistency between Dice = 92.3% (Tables III/IV) and average Dice = 0.58 (Table VI) is a serious correctness problem but is not circularity, because no derivation in the paper forces those numbers to be equal. The comparison against MLP and KAN is independent of the stacking rule's definition. Hence no specific circular step can be exhibited under the hard rules.

Assumptions & free parameters 6 free parameters · 3 assumptions · 0 invented entities

proKAN introduces no new physical entities; its load-bearing content is a set of hand-chosen hyperparameters and the unvalidated assumption that adding capacity during validation plateau reduces overfitting.

free parameters (6)
  • Grid increment ΔG = not specified
    Grid size grows by a constant ΔG as blocks are added (Table II); value chosen by hand, affects model expressiveness.
  • Spline degree increment Δk = not specified
    Degree of B-splines increases by Δk per block (Table II); hand-chosen, controls smoothness.
  • Learning rate decay factor α = not specified
    Learning rate updated as η_b = η_{b-1} / (1 + α b) (Table II); α is a hand-selected decay.
  • Regularization increment Δλ = not specified
    Regularization coefficient increased by Δλ as blocks are added (Table II).
  • Plateau threshold ε = not specified
    Used in the condition ΔL_val < ε to trigger block addition (Section III-B1).
  • Plateau window t_plateau = not specified
    Number of epochs over which validation loss is averaged in the plateau check (Section III-B2).
assumptions (3)
  • standard math Kolmogorov-Arnold representation theorem permits representing any continuous multivariate function as a finite composition of univariate functions.
    Invoked in Section III-A1 as the foundation for KANs; accepted theorem, but the finite-depth approximation with B-splines is an approximation not guaranteed by the theorem.
  • domain assumption The LiTS17 ground-truth segmentations are reliable and the train/validation split is representative.
    Used implicitly in Section IV-A; the paper does not report how data was split for the reported tables.
  • ad hoc to paper Adding KAN blocks when validation loss plateaus while training loss decreases will mitigate, rather than exacerbate, overfitting.
    Core heuristic of proKAN stated in Section III-B; no theoretical or empirical support beyond the paper's own, contradictory, tables.

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Cite this review

Pith. "Pith review of ProKAN: Progressive Stacking of Kolmogorov-Arnold Networks for Efficient Liver Segmentation." pith.science (2026). https://pith.science/paper/AMWEBCTX

@misc{pith2026241219713,
  author       = {Pith},
  title        = {Pith review of: ProKAN: Progressive Stacking of Kolmogorov-Arnold Networks for Efficient Liver Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AMWEBCTX}},
  note         = {Machine review of arXiv:2412.19713}
}
read the original abstract

The growing need for accurate and efficient 3D identification of tumors, particularly in liver segmentation, has spurred considerable research into deep learning models. While many existing architectures offer strong performance, they often face challenges such as overfitting and excessive computational costs. An adjustable and flexible architecture that strikes a balance between time efficiency and model complexity remains an unmet requirement. In this paper, we introduce proKAN, a progressive stacking methodology for Kolmogorov-Arnold Networks (KANs) designed to address these challenges. Unlike traditional architectures, proKAN dynamically adjusts its complexity by progressively adding KAN blocks during training, based on overfitting behavior. This approach allows the network to stop growing when overfitting is detected, preventing unnecessary computational overhead while maintaining high accuracy. Additionally, proKAN utilizes KAN's learnable activation functions modeled through B-splines, which provide enhanced flexibility in learning complex relationships in 3D medical data. Our proposed architecture achieves state-of-the-art performance in liver segmentation tasks, outperforming standard Multi-Layer Perceptrons (MLPs) and fixed KAN architectures. The dynamic nature of proKAN ensures efficient training times and high accuracy without the risk of overfitting. Furthermore, proKAN provides better interpretability by allowing insight into the decision-making process through its learnable coefficients. The experimental results demonstrate a significant improvement in accuracy, Dice score, and time efficiency, making proKAN a compelling solution for 3D medical image segmentation tasks.

Figures

Figures reproduced from arXiv: 2412.19713 by the authors.

Figure 1
Figure 1. Overall Workflow for Liver Segmentation: The diagram depicts the full pipeline from input CT scan to the final segmented liver tumor output. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Kolmogorov-Arnold Network (KAN) Architecture: This figure illustrates the architecture of a KAN block used in the proKAN model. Each edge is [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Example CT scans from the LiTS17 dataset showcasing liver tumor regions. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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