Implicit U-KAN2.0: Dynamic, Efficient and Interpretable Medical Image Segmentation

2025-03-05

AI Summary

Existing medical image segmentation methods suffer from poor interpretability, weak noise robustness, and limited representational capacity due to reliance on discrete hierarchical architectures and insufficient theoretical foundations. To address these limitations, we propose U-KAN2.0, an implicit U-shaped network featuring a novel two-stage encoder-decoder architecture that integrates second-order neural ordinary differential equations (SONO) with multi-scale Kolmogorov–Arnold networks (MultiKAN), enabling continuous-depth modeling and dynamic feature evolution. We theoretically prove that MultiKAN’s universal approximation capability is dimensionality-agnostic—overcoming the inherent constraints of discrete-layered networks. Evaluated on multiple 2D and one 3D medical image datasets, U-KAN2.0 achieves state-of-the-art performance with significantly fewer parameters and faster inference speed compared to U-Net, TransUNet, and other leading models—demonstrating superior accuracy, enhanced expressivity, and improved interpretability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Segmentation
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Improves interpretability and performance in medical image segmentation.
• Addresses limitations of U-Net variants with a novel two-phase encoder-decoder structure.
• Reduces computational costs while enhancing representation power and noise handling.

Innovation

• Implicit U-KAN 2.0 with two-phase encoder-decoder structure
• SONO block using second-order neural ODEs
• MultiKAN layer enhances interpretability and representation