GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling

arXiv:2511.05477v2 Announce Type: replace 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.