Fully Kolmogorov-Arnold Deep Model in Medical Image Segmentation

Deeply stacked KANs are practically impossible due to high training difficulties and substantial memory requirements. Consequently, existing studies can only incorporate few KAN layers, hindering the comprehensive exploration of KANs. This study overcomes these limitations and introduces the first fully KA-based deep model, demonstrating that KA-based layers can entirely replace traditional architectures in deep learning and achieve superior learning capacity. Specifically, (1) the proposed Share-activation KAN (SaKAN) reformulates Sprecher's variant of Kolmogorov-Arnold representation theorem, which achieves better optimization due to its simplified parameterization and denser training samples, to ease training difficulty, (2) this paper indicates that spline gradients contribute negligibly to training while consuming huge GPU memory, thus proposes the Grad-Free Spline to significantly reduce memory usage and computational overhead. (3) Building on these two innovations, our ALL U-KAN is the first representative implementation of fully KA-based deep model, where the proposed KA and KAonv layers completely replace FC and Conv layers. Extensive evaluations on three medical image segmentation tasks confirm the superiority of the full KA-based architecture compared to partial KA-based and traditional architectures, achieving all higher segmentation accuracy. Compared to directly deeply stacked KAN, ALL U-KAN achieves 10 times reduction in parameter count and reduces memory consumption by more than 20 times, unlocking the new explorations into deep KAN architectures.