# GroupKAN: Efficient Kolmogorov-Arnold Networks via Grouped Spline Modeling

arXiv: https://arxiv.org/abs/2511.05477 · HTML: https://mlsanity.com/paper/2511.05477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [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)
- [Embracing Imperfect Datasets: A Review of Deep Learning Solutions for Medical Image Segmentation](https://mlsanity.com/paper/1908.10454/) (2019)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [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)
- [Medical Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2009.13120/) (2020)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [A Practical Survey on Faster and Lighter Transformers](https://mlsanity.com/paper/2103.14636/) (2021)
- [Kolmogorov-Arnold Convolutions: Design Principles and Empirical Studies](https://mlsanity.com/paper/2407.01092/) (2024)
- [A Comprehensive Survey of Convolutions in Deep Learning: Applications, Challenges, and Future Trends](https://mlsanity.com/paper/2402.15490/) (2024)
- [Gompertz Linear Units: Leveraging Asymmetry for Enhanced Learning Dynamics](https://mlsanity.com/paper/2502.03654/) (2025)

## Abstract (arXiv)

Medical image segmentation demands models that achieve high accuracy while maintaining computational efficiency and clinical interpretability. While recent Kolmogorov-Arnold Networks (KANs) offer powerful adaptive non-linearities, their full-channel spline transformations incur a quadratic parameter growth of O(C2(G+k)) with respect to the channel dimension C, where G and k denote the number of grid intervals and spline polynomial order, respectively. Moreover, unconstrained spline mappings lack structural constraints, leading to excessive functional freedom, which may cause overfitting under limited medical annotations. To address these challenges, we propose GroupKAN (Grouped Kolmogorov-Arnold Networks), an efficient architecture driven by group-structured spline modeling. Specifically, we introduce: (1) Grouped KAN Transform (GKT), which restricts spline interactions to intra-group channel mappings across g groups, effectively reducing the spline-induced quadratic expansion to textbfO(C2(fracG+kg + 1)), thereby significantly lowering the effective quadratic coefficient; and (2) Grouped KAN Activation (GKA), which applies shared spline functions within each group to enable efficient token-wise non-linearities. By imposing structured constraints on channel interactions, GroupKAN achieves a substantial reduction in parameter redundancy without sacrificing expressive capacity.Extensive evaluations on three medical benchmarks (BUSI, GlaS, and CVC) demonstrate that GroupKAN achieves an average IoU of 79.80%, outperforming the strong U-KAN baseline by +1.11% while requiring only 47.6% of the parameters (3.02M vs. 6.35M). Qualitative results further reveal that GroupKAN produces sharply localized activation maps that better align with the ground truth than MLPs and KANs, significantly enhancing clinical interpretability.