DEQ-KAN: Deep equilibrium Kolmogorov–Arnold networks for robust classification

Abstract

We present DEQ-KAN, a novel deep learning architecture for medical image classification that integrates deep equilibrium models (DEQs) with Kolmogorov–Arnold networks (KANs) to enhance classification accuracy and model robustness. DEQ allows for infinite-depth modeling through iterative refinement, while KAN facilitates the learning of univariate transformations, improving expressivity. We evaluate DEQ-KAN on three challenging tasks: pneumonia detection from X-ray images, multi-class tumor recognition from MRI scans, and benign-versus-malignant classification in breast histopathology images. Our results demonstrate that DEQ-KAN outperforms state-of-the-art models across multiple performance metrics and exhibits strong generalization, particularly in multi-class, imbalanced, and small-image-size scenarios. Ablation studies highlight the critical contributions of both DEQ’s iterative process and KAN’s expansions in achieving superior classification outcomes. These findings suggest that DEQ-KAN is well-suited for deployment in high-stakes medical imaging applications, where accuracy and reliability are paramount.