GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling

Medical image segmentation requires models that balance accuracy, computational efficiency, and qualitative interpretability. Recent Kolmogorov-Arnold Networks (KANs) provide adaptive nonlinearities, but full-channel spline transformations incur quadratic parameter growth 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. Unconstrained spline mappings also lack structural constraints, producing excessive functional freedom that may overfit limited medical annotations. To address these challenges, we propose GroupKAN (Grouped Kolmogorov-Arnold Networks), an efficient architecture based on groupstructured spline modeling. It introduces: (1) Grouped KAN Transform (GKT), which restricts spline interactions to intra-group channel mappings across g groups and reduces the spline-induced quadratic expansion to O(C^2((G+k)/g + 1)); and (2) Grouped KAN Activation (GKA), which applies shared spline functions within each group for efficient tokenwise nonlinear functions. These structural constraints reduce parameter redundancy while preserving expressive capacity. On BUSI, GlaS, and CVC, GroupKAN achieves an average IoU of 79.80%, outperforming UKAN by +1.11% while using only 47.6% of its parameters (3.02M vs. 6.35M). Qualitative results further show more localized activation maps than MLPs and KANs, supporting its interpretable activation behavior.