Title: FunKAN: Functional Kolmogorov-Arnold Network for Medical Image Segmentation
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Kolmogorov-Arnold networks, Hermite functions, Image segmentation, Medical imaging

Abstract: Medical image segmentation is pivotal for clinical diagnosis, however, remains challenging due to complex anatomies and imaging artifacts.
While deep learning offers powerful solutions, prevailing architectures lack inherent interpretability and often rely on empirically designed components.
Kolmogorov-Arnold networks provide a mathematically interpretable alternative but fail to preserve the spatial structure of visual data, as they process flattened feature vectors.
To bridge this gap, we introduce Functional Kolmogorov-Arnold Network (FunKAN), a novel framework that generalizes the Kolmogorov-Arnold theorem to functional spaces.
FunKAN parameterizes its inner functions via truncated spectral expansion over Hermite basis functions, enabling direct processing of 2D feature maps within a theoretically grounded, interpretable design. Leveraging this, we integrate FunKAN into the U-shaped architecture, yielding a new state-of-the-art segmentation model across diverse medical imaging modalities.
Extensive benchmarks on BUSI (ultrasound), GlaS (histology), and CVC-ClinicDB (colonoscopy) datasets show
that U-FunKAN outperforms strong baselines (U-Net, KAN, Mamba), achieving IoU and F1-score improvement and superior efficiency in terms of Gflops.
Our work unites theoretical function approximation and practical medical image analysis, offering the novel state-of-the-art solution for clinical applications.