GroupKAN: Rethinking Nonlinearity with Grouped Spline-based KAN Modeling for Efficient Medical Image Segmentation

Abstract: Medical image segmentation requires models that are accurate, lightweight, and interpretable. Convolutional architectures lack adaptive nonlinearity and transparent decision-making, whereas Transformer architectures are hindered by quadratic complexity and opaque attention mechanisms. U-KAN addresses these challenges using Kolmogorov-Arnold Networks, achieving higher accuracy than both convolutional and attention-based methods, fewer parameters than Transformer variants, and improved interpretability compared to conventional approaches. However, its O(C^2) complexity due to full-channel transformations limits its scalability as the number of channels increases. To overcome this, we introduce GroupKAN, a lightweight segmentation network that incorporates two novel, structured functional modules: (1) Grouped KAN Transform, which partitions channels into G groups for multivariate spline mappings, reducing complexity to O(C^2/G), and (2) Grouped KAN Activation, which applies shared spline-based mappings within each channel group for efficient, token-wise nonlinearity. Evaluated on three medical benchmarks (BUSI, GlaS, and CVC), GroupKAN achieves an average IoU of 79.80 percent, surpassing U-KAN by +1.11 percent while requiring only 47.6 percent of the parameters (3.02M vs 6.35M), and shows improved interpretability.