# Fully Kolmogorov-Arnold Deep Model in Medical Image Segmentation

arXiv: https://arxiv.org/abs/2602.03156 · HTML: https://mlsanity.com/paper/2602.03156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [Medical Transformer: Gated Axial-Attention for Medical Image Segmentation](https://mlsanity.com/paper/2102.10662/) (2021)
- [UNeXt: MLP-based Rapid Medical Image Segmentation Network](https://mlsanity.com/paper/2203.04967/) (2022)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem](https://mlsanity.com/paper/1906.11945/) (2019)
- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
- [SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series](https://mlsanity.com/paper/2406.17890/) (2024)
- [Finding Local Diffusion Schr"odinger Bridge using Kolmogorov-Arnold Network](https://mlsanity.com/paper/2502.19754/) (2025)
- [Implicit U-KAN2.0: Dynamic, Efficient and Interpretable Medical Image Segmentation](https://mlsanity.com/paper/2503.03141/) (2025)

## Abstract (arXiv)

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.