Image segmentation is a fundamental task in both image analysis and medical applications. State-of-the-art methods predominantly rely on encoder-decoder architectures with a U-shaped design, commonly referred to as U-Net. Recent advancements integrating transformers and MLPs improve performance but still face key limitations, such as poor interpretability, difficulty handling intrinsic noise, and constrained expressiveness due to discrete layer structures, often lacking a solid theoretical foundation.In this work, we introduce Implicit U-KAN 2.0, a novel U-Net variant that adopts a two-phase encoder-decoder structure. In the SONO phase, we use a second-order neural ordinary differential equation (NODEs), called the SONO block, for a more efficient, expressive, and theoretically grounded modeling approach. In the SONO-MultiKAN phase, we integrate the second-order NODEs and MultiKAN layer as the core computational block to enhance interpretability and representation power. Our contributions are threefold. First, U-KAN 2.0 is an implicit deep neural network incorporating MultiKAN and second order NODEs, improving interpretability and performance while reducing computational costs. Second, we provide a theoretical analysis demonstrating that the approximation ability of the MultiKAN block is independent of the input dimension. Third, we conduct extensive experiments on a variety of 2D and a single 3D dataset, demonstrating that our model consistently outperforms existing segmentation networks. Project Website: https://math-ml-x.github.io/IUKAN2/

翻译：图像分割是图像分析和医学应用中的一项基础任务。当前最先进的方法主要依赖于具有U形设计的编码器-解码器架构，通常被称为U-Net。近期整合Transformer和MLP的进展提升了性能，但仍面临关键局限，例如可解释性差、难以处理固有噪声，以及离散层结构导致的表达能力受限，且往往缺乏坚实的理论基础。在本工作中，我们提出了隐式U-KAN 2.0，一种新颖的U-Net变体，采用两阶段编码器-解码器结构。在SONO阶段，我们使用称为SONO块的二阶神经常微分方程（NODEs），以实现更高效、更具表达力且理论依据更充分的建模方法。在SONO-MultiKAN阶段，我们整合二阶NODEs和MultiKAN层作为核心计算块，以增强可解释性和表示能力。我们的贡献有三方面。首先，U-KAN 2.0是一个融合了MultiKAN和二阶NODEs的隐式深度神经网络，在提高可解释性和性能的同时降低了计算成本。其次，我们提供了理论分析，证明MultiKAN块的逼近能力与输入维度无关。第三，我们在多种2D数据集和一个3D数据集上进行了广泛实验，结果表明我们的模型在分割任务上持续优于现有网络。项目网站：https://math-ml-x.github.io/IUKAN2/