基于动态Kolmogorov-Arnold网络与自适应非线性建模的医学图像分割

Medical Image Segmentation Based on Dynamic Kolmogorov-Arnold Network and Adaptive Nonlinear Modeling

摘要: 针对医学图像分割中复杂非线性模式的精确捕获、模型可解释性以及传统固定非线性激活函数局限性的挑战，本文提出了一种新型的动态Kolmogorov-Arnold网络U-Net (Dynamic KAN UNet, DKAN-UNet)。该网络在经典的U-Net编码器–解码器架构基础上，引入了创新的动态KAN模块(DKAN Block)，旨在实现特征依赖的自适应非线性建模。具体而言，DKAN Block包含一个轻量级的非线性适应单元(Non-linearity Adaptation Unit, NAU)，该单元能够根据输入特征的局部特性，动态地调整KAN层中可学习激活函数的参数(如B-spline基函数的网格点或系数)，从而为不同区域和语义信息提供定制化的非线性变换。此外，我们设计了多尺度动态KAN融合策略，在编码器和解码器中部署DKAN Block，并通过跳跃连接实现多尺度特征的自适应非线性交互。实验结果表明，DKAN-UNet在多个医学图像分割数据集上取得了显著优于现有U-KAN等方法的性能，同时显著增强了模型的非线性建模能力和可解释性。

Abstract: To address the challenges of accurately capturing complex nonlinear patterns, model interpretability, and the limitations of traditional fixed nonlinear activation functions in medical image segmentation, this paper proposes a novel Dynamic Kolmogorov-Arnold Network U-Net (Dynamic KAN UNet, DKAN-UNet). This network builds upon the classic U-Net encoder-decoder architecture by introducing an innovative Dynamic KAN module (DKAN Block), aiming to achieve feature-dependent adaptive nonlinear modeling. Specifically, the DKAN Block incorporates a lightweight Non-linearity Adaptation Unit (NAU), which can dynamically adjust the parameters of the learnable activation function in the KAN layer (such as the grid points or coefficients of the B-spline basis functions) based on the local characteristics of the input features, thereby providing customized nonlinear transformations for different regions and semantic information. Additionally, we have designed a multi-scale dynamic KAN fusion strategy, deploying DKAN Blocks in both the encoder and decoder and achieving adaptive nonlinear interaction of multi-scale features through skip connections. Experimental results demonstrate that DKAN-UNet achieves significantly superior performance on multiple medical image segmentation datasets compared to existing methods such as U-KAN, while significantly enhancing the model’s nonlinear modeling capability and interpretability.