AttFKAN-DEQ: Attention-Enhanced Fourier Kolmogorov-Arnold Networks Using Deep Equilibrium for Breast Cancer Histopathology Classification

Breast cancer histopathological classification remains a challenging task due to small patch resolution, staining inconsistencies, magnification variability, and class imbalance in datasets such as BreakHis and IDC, which hinder accurate malignancy detection. This paper proposes AttFKAN-DEQ, a novel framework that integrates Fourier Kolmogorov-Arnold Networks (FKANs) with Deep Equilibrium Models (DEQs) for binary benign-versus-malignant classification. Unlike spline-based formulations, FKANs model univariate edge functions using finite trigonometric series with trainable sine and cosine coefficients, enabling robust multi-scale spectral representations of heterogeneous tissue morphology. To enhance feature discrimination, a Lightweight Convolutional Block Attention Module (LCBAM) is incorporated within the FKAN residual block to perform channel-wise and spatial feature recalibration during each DEQ iteration using depthwise separable convolutions. This mechanism emphasizes diagnostically relevant regions while suppressing irrelevant background variations. Furthermore, the DEQ mechanism implicitly models infinite network depth through fixed-point iterations at constant memory cost, allowing stable and progressive latent feature refinement. The proposed framework was evaluated using five-fold stratified cross-validation with standard data augmentation. AttFKAN-DEQ achieved 96.60% accuracy and 98.44% AUC on the BreakHis dataset and 94.52% accuracy with 97.31% AUC on the IDC dataset. Experimental results demonstrate that the proposed model outperforms DEQ-KAN, ResNet variants, DenseNet-121, EfficientNet-B0, Vision Transformer, Swin Transformer, ConvNeXt, and MobileViT across multiple evaluation metrics. Ablation studies further confirm the individual and combined contributions of Fourier parameterization, lightweight attention, and equilibrium-based feature refinement to the overall performance. Despite containing only 6.0M parameters and requiring 0.60 GFLOPs, AttFKAN-DEQ achieves high diagnostic accuracy with strong computational efficiency, highlighting its potential for deployment in real-world clinical histopathology applications.