MedKAFormer: When Kolmogorov-Arnold Theorem Meets Vision Transformer for Medical Image Representation

Area of Science:

• Artificial Intelligence
• Medical Image Analysis
• Deep Learning Architectures

Background:

• Vision Transformers (ViTs) exhibit high parameter complexity due to reliance on Multi-layer Perceptrons (MLPs), hindering medical image analysis with limited data.
• Existing ViT optimization methods struggle to balance effective modeling, parameter efficiency, and data availability in the medical domain.
• Kolmogorov-Arnold Networks (KANs) offer an alternative to MLPs but face integration challenges with ViTs for 2D structured medical data.

Purpose of the Study:

• To propose MedKAFormer, the first Vision Transformer (ViT) model integrating the Kolmogorov-Arnold (KA) theorem for enhanced medical image representation.
• To overcome the limitations of directly applying KANs to ViTs, addressing 2D data handling and dimensionality issues.
• To reduce parameter complexity and improve feature representation in ViTs for medical imaging tasks.

Main Methods:

• Introduction of a Dynamic Kolmogorov-Arnold Convolution (DKAC) layer for flexible nonlinear modeling during patch embedding.
• Incorporation of a Nonlinear Sparse Token Mixer (NSTM) and a Nonlinear Dynamic Filter (NDF) in the non-embedding stage for comprehensive nonlinear representation.
• Development of MedKAFormer as a novel ViT architecture tailored for medical image analysis.

Main Results:

• MedKAFormer achieves an 85.61% reduction in parameter complexity compared to ViT-Base.
• The model demonstrates competitive performance across 14 diverse medical datasets, encompassing various imaging modalities and anatomical structures.
• The proposed components effectively reduce model overfitting while enhancing nonlinear representation capabilities.

Conclusions:

• MedKAFormer presents a significant advancement in developing parameter-efficient Vision Transformers for medical image analysis.
• The integration of the Kolmogorov-Arnold theorem offers a promising direction for overcoming the limitations of traditional ViT architectures in data-scarce medical settings.
• The model's effectiveness across multiple datasets and modalities highlights its potential for broad clinical application.