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arxiv: 2511.05477 · v2 · submitted 2025-11-07 · 💻 cs.CV

GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling

Guojie Li , Tianyi Liu , Anwar P.P. Abdul Majeed , Muhammad Ateeq , Anh Nguyen , Fan Zhang This is my paper

Pith reviewed 2026-05-17 23:26 UTC · model grok-4.3

classification 💻 cs.CV
keywords Kolmogorov-Arnold NetworksMedical Image SegmentationEfficient ArchitecturesSpline ModelingGrouped InteractionsParameter ReductionU-KAN
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The pith

GroupKAN restricts spline interactions within channel groups to reduce parameter growth in Kolmogorov-Arnold Networks for medical segmentation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Kolmogorov-Arnold Networks offer adaptive nonlinear transformations but their full spline mappings cause quadratic parameter growth with increasing channels, which becomes impractical for medical image segmentation where data is limited. The paper proposes GroupKAN to divide channels into groups and limit the spline mappings to occur only within each group. This structured constraint lowers the parameter scaling while still allowing the network to learn effective nonlinearities for segmentation. Tests on breast ultrasound, gland, and colorectal polyp datasets show GroupKAN reaching an average IoU of 79.80% with 3.02 million parameters, surpassing the previous KAN model that used 6.35 million parameters. The grouped design also leads to activation maps that more precisely highlight the target structures in the images.

Core claim

By introducing the Grouped KAN Transform that computes splines only for intra-group channel pairs across a chosen number of groups and the Grouped KAN Activation that shares spline functions inside each group, GroupKAN achieves a parameter reduction to roughly half while delivering superior segmentation performance on standard medical benchmarks.

What carries the argument

Grouped KAN Transform (GKT) that restricts spline interactions to intra-group channel mappings across g groups, reducing the quadratic term by a factor related to the group count.

If this is right

  • Models for medical image analysis can achieve better accuracy with reduced computational resources and memory footprint.
  • Activation maps become more localized and interpretable, aiding clinical review of model decisions.
  • The approach enables KAN layers to be incorporated into larger segmentation networks without exceeding hardware limits.
  • Overfitting risks decrease because the constrained interactions limit unnecessary functional complexity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Grouping strategies like this may help control complexity in other types of basis expansion networks beyond KANs.
  • Applying the same intra-group restriction to vision transformers or CNNs could yield similar efficiency gains in other tasks.
  • Future work might explore adaptive group sizes that depend on channel importance rather than fixed divisions.

Load-bearing premise

That restricting spline interactions to intra-group channel mappings preserves sufficient expressive capacity for medical segmentation without meaningful performance loss.

What would settle it

Measuring the IoU of GroupKAN on the BUSI dataset when the number of groups is increased to match the total number of channels, which should approach the performance of the full unconstrained KAN or fall below it if the assumption fails.

Figures

Figures reproduced from arXiv: 2511.05477 by Anh Nguyen, Anwar P.P. Abdul Majeed, Fan Zhang, Guojie Li, Muhammad Ateeq, Tianyi Liu.

Figure 1
Figure 1. Figure 1: Accuracy–complexity trade-off in medical segmentation: IoU (%) vs. number of parameters (M) among [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the GroupKAN pipeline. The encoder extracts features through convolutional blocks. In the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of Grouped KAN Activation. Given token embeddings [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of Grouped KAN Transform. The input feature [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative comparison of segmentation results on BUSI, GlaS, and CVC-ClinicDB. GroupKAN produces [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: 3D visualization of IoU and parameter count across [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Channel activation maps for explainability comparison. GroupKAN with GKT (bottom-left) shows the best [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

Medical image segmentation demands models that achieve high accuracy while maintaining computational efficiency and clinical interpretability. While recent Kolmogorov-Arnold Networks (KANs) offer powerful adaptive non-linearities, their full-channel spline transformations incur a quadratic parameter growth of $\mathcal{O}(C^{2}(G+k))$ with respect to the channel dimension $C$, where $G$ and $k$ denote the number of grid intervals and spline polynomial order, respectively. Moreover, unconstrained spline mappings lack structural constraints, leading to excessive functional freedom, which may cause overfitting under limited medical annotations. To address these challenges, we propose GroupKAN (Grouped Kolmogorov-Arnold Networks), an efficient architecture driven by group-structured spline modeling. Specifically, we introduce: (1) Grouped KAN Transform (GKT), which restricts spline interactions to intra-group channel mappings across $g$ groups, effectively reducing the spline-induced quadratic expansion to \textbf{$\mathcal{O}(C^2(\frac{G+k}{g} + 1))$}, thereby significantly lowering the effective quadratic coefficient; and (2) Grouped KAN Activation (GKA), which applies shared spline functions within each group to enable efficient token-wise non-linearities. By imposing structured constraints on channel interactions, GroupKAN achieves a substantial reduction in parameter redundancy without sacrificing expressive capacity.Extensive evaluations on three medical benchmarks (BUSI, GlaS, and CVC) demonstrate that GroupKAN achieves an average IoU of 79.80\%, outperforming the strong U-KAN baseline by +1.11\% while requiring only 47.6\% of the parameters (3.02M vs. 6.35M). Qualitative results further reveal that GroupKAN produces sharply localized activation maps that better align with the ground truth than MLPs and KANs, significantly enhancing clinical interpretability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes GroupKAN for efficient medical image segmentation using Kolmogorov-Arnold Networks. It introduces Grouped KAN Transform (GKT) to restrict spline interactions within channel groups, reducing parameter scaling to O(C²((G+k)/g +1)), and Grouped KAN Activation (GKA) for shared intra-group activations. On BUSI, GlaS, and CVC benchmarks, it reports 79.80% average IoU, +1.11% over U-KAN, with 47.6% parameters (3.02M vs. 6.35M), claiming better interpretability.

Significance. GroupKAN addresses the quadratic parameter growth in KANs through structured grouping, which if the modest performance gains prove robust, could facilitate wider adoption of KANs in efficient and interpretable medical segmentation models. The approach provides a concrete mechanism to trade off interaction density for computational savings while maintaining or improving accuracy on the tested datasets.

major comments (3)
  1. [Abstract] The reported average IoU of 79.80% and +1.11% improvement lack accompanying error bars, results from multiple random seeds, or p-values from statistical tests. Without these, the claim of outperforming U-KAN without sacrificing accuracy cannot be fully substantiated, as the central efficiency-without-loss assertion relies on these empirical results.
  2. [Methods (GKT definition)] The GKT partitions channels into g groups and applies intra-group splines, yielding the reduced complexity. However, this implicitly assumes later layers or GKA can recover necessary inter-group non-linearities for precise boundary segmentation in medical images. No analysis of cross-group feature interactions or sensitivity to g is provided, which is load-bearing for whether expressive capacity is preserved.
  3. [Experiments] No ablation experiments are described varying the group count g, despite it being a key free parameter that controls the efficiency-capacity trade-off. Including such ablations would directly test the weakest assumption that intra-group restriction does not lead to meaningful performance loss.
minor comments (2)
  1. [Abstract] The complexity expression uses G and k for grid and order; ensure these are consistently defined and referenced in the main text with equation numbers.
  2. [Qualitative results] The claim of 'sharply localized activation maps' would benefit from quantitative metrics comparing alignment with ground truth, such as activation overlap scores, rather than relying solely on qualitative description.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, agreeing where appropriate and outlining specific revisions to strengthen the empirical support and analysis.

read point-by-point responses

  1. Referee: [Abstract] The reported average IoU of 79.80% and +1.11% improvement lack accompanying error bars, results from multiple random seeds, or p-values from statistical tests. Without these, the claim of outperforming U-KAN without sacrificing accuracy cannot be fully substantiated, as the central efficiency-without-loss assertion relies on these empirical results.

    Authors: We agree that statistical rigor is essential for validating the reported performance gains. In the revised manuscript, we will augment the abstract and results sections with mean IoU and standard deviations computed over multiple random seeds (at least five runs), along with p-values from paired statistical tests comparing GroupKAN against the U-KAN baseline. This will provide stronger substantiation for the efficiency-without-loss claim. revision: yes

  2. Referee: [Methods (GKT definition)] The GKT partitions channels into g groups and applies intra-group splines, yielding the reduced complexity. However, this implicitly assumes later layers or GKA can recover necessary inter-group non-linearities for precise boundary segmentation in medical images. No analysis of cross-group feature interactions or sensitivity to g is provided, which is load-bearing for whether expressive capacity is preserved.

    Authors: The referee correctly identifies a key implicit assumption in the GKT design. While the architecture relies on subsequent convolutional layers and the overall network depth to integrate cross-group information hierarchically, we will revise the Methods section to include a dedicated discussion of cross-group feature recovery. We will also add a sensitivity analysis subsection examining performance as a function of g to demonstrate that expressive capacity for boundary segmentation is preserved across reasonable group counts. revision: partial

  3. Referee: [Experiments] No ablation experiments are described varying the group count g, despite it being a key free parameter that controls the efficiency-capacity trade-off. Including such ablations would directly test the weakest assumption that intra-group restriction does not lead to meaningful performance loss.

    Authors: We fully agree that ablations on the group count g are required to rigorously validate the core design trade-off. In the revised Experiments section, we will add comprehensive ablation studies varying g (including values such as 1, 2, 4, and 8) and report the resulting IoU scores, parameter counts, and efficiency metrics on all three benchmarks. These results will directly address whether intra-group restrictions incur meaningful performance degradation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; efficiency scaling follows directly from explicit grouping definition and is validated empirically

full rationale

The paper introduces GKT and GKA by defining intra-group spline restrictions (g groups) and derives the reduced complexity O(C²((G+k)/g +1)) as a direct algebraic consequence of that architectural choice. Reported gains (+1.11% IoU, 47.6% parameters) are measured against external baselines (U-KAN) on independent datasets rather than obtained by fitting or renaming within the paper. No load-bearing step reduces to self-citation, fitted prediction, or self-definition; the derivation remains self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The design rests on the premise that channel grouping imposes useful structural constraints while retaining enough non-linearity; the number of groups is treated as a tunable hyperparameter.

free parameters (1)
  • number of groups g
    Hyperparameter that controls the degree of parameter reduction versus retained expressivity; its specific value is chosen to achieve the reported efficiency gains.
axioms (1)
  • domain assumption Intra-group spline mappings suffice to model the channel interactions required for accurate medical segmentation
    Invoked to justify restricting interactions to within groups in the GKT definition.

pith-pipeline@v0.9.0 · 5657 in / 1221 out tokens · 36260 ms · 2026-05-17T23:26:57.861351+00:00 · methodology

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Reference graph

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