Authors - Binh Pham Nguyen Thanh, Chau M. Truong, Nhan Thi Cao Abstract - ResNet is widely used in medical image classification due to its strong hierarchical feature extraction capability. This study investigates the integration of Kolmogorov–Arnold Networks (KAN) and ConvKAN into ResNet to analyze the effect of increasing nonlinearity at different stages within a hierarchical skin lesion classification framework. Convolutional KAN is applied at the initial layer to enhance low-level feature extraction, while KAN is introduced at the final layer to improve high-level decision boundary modeling. A combined configuration is also evaluated to examine potential complementary effects across different levels of label granularity. Results show that performance depends on both the integration stage and dataset characteristics. Convolutional KAN at early layers provides limited and inconsistent improvements, whereas KAN at the final layer yields more stable gains. In addition, models incorporating KAN-based architectures generally achieve better performance across metrics such as accuracy, precision, F1-score, and ROC AUC. As classification becomes more fine-grained, Recall consistently decreases despite high ROC AUC, indicating challenges in decision thresholding across hierarchical levels. Overall, KAN is more effective for high-level decision making, while dataset complexity has a greater impact than architectural modifications.