GroupKAN通过分组样条建模，让医学图像分割更准更快且可解释。
GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling
- 将通道分组限制样条交互，降低参数量级
- 在三个数据集上平均交并比达79.80%，参数仅需原模型47.6%
- 激活图更聚焦，适合临床医生理解
医学图像分割需要高精度、低计算开销且具备临床可解释性的模型。近期的科尔莫戈罗夫-阿诺德网络（KANs）虽具强大自适应非线性能力，但全通道样条变换导致参数量随通道数 $C$ 呈二次增长，形式为 $/mathcal{O}(C^{2}(G+k))$，其中 $G$ 和 $k$ 分别为网格区间数与样条多项式阶数。此外，无约束样条映射功能自由度过高，在有限医疗标注下易过拟合。为此，我们提出 GroupKAN（分组科尔莫戈罗夫-阿诺德网络），基于分组结构样条建模。具体包括：(1) 分组KAN变换（GKT），将样条交互限制于 $g$ 个组内通道间，将二次膨胀降至 $ extbf{/mathcal{O}(C^2( rac{G+k}{g} + 1))}$，显著降低有效二次系数；(2) 分组KAN激活（GKA），组内共享样条函数，实现高效逐标记非线性。通过结构化约束通道交互，GroupKAN大幅减少参数冗余而不损失表达能力。在三个人类医学基准（BUSI、GlaS、CVC）上的广泛评估表明，GroupKAN平均交并比达79.80%，优于强基线U-KAN的+1.11%，同时仅需其47.6%参数（3.02M vs. 6.35M）。定性结果进一步显示，GroupKAN生成的激活图更尖锐聚焦，与真实标签对齐度更高，显著提升临床可解释性。
原文摘要 · Abstract (English)
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.
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