This paper explores the application of Kolmogorov-Arnold Networks (KANs) in computer vision, focusing on convolutional KANs and their variants. The authors propose a parameter-efficient design for Kolmogorov-Arnold convolutional layers and a fine-tuning algorithm for pre-trained KAN models. They evaluate these methods on various datasets, including MNIST, CIFAR10, CIFAR100, Tiny ImageNet, ImageNet1K, and HAM10000 for image classification, and BUSI, GlaS, and CVC for segmentation tasks. Key contributions include: 1. **Bottleneck Convolutional Kolmogorov-Arnold Layers**: These layers reduce memory requirements and mitigate overfitting issues. 2. **Parameter-Efficient Fine-Tuning Algorithm**: This algorithm significantly reduces the number of trainable parameters needed for adapting pre-trained models to new tasks. 3. **Regularization Techniques**: The paper investigates various regularization techniques, including weight and activation penalties, dropout placements, and additive Gaussian noise injection. 4. **Self-KAGNAttention Layers**: These layers enhance model performance, particularly in complex tasks. The authors conclude that KAN-based convolutional models can achieve state-of-the-art results in both classification and segmentation tasks, highlighting the effectiveness of Gram polynomials as the basis function and the advantages of scaling model width over depth. They also provide design principles for constructing successful KAN convolutional models and suggest future research directions, including refining these approaches and exploring additional regularization techniques.This paper explores the application of Kolmogorov-Arnold Networks (KANs) in computer vision, focusing on convolutional KANs and their variants. The authors propose a parameter-efficient design for Kolmogorov-Arnold convolutional layers and a fine-tuning algorithm for pre-trained KAN models. They evaluate these methods on various datasets, including MNIST, CIFAR10, CIFAR100, Tiny ImageNet, ImageNet1K, and HAM10000 for image classification, and BUSI, GlaS, and CVC for segmentation tasks. Key contributions include: 1. **Bottleneck Convolutional Kolmogorov-Arnold Layers**: These layers reduce memory requirements and mitigate overfitting issues. 2. **Parameter-Efficient Fine-Tuning Algorithm**: This algorithm significantly reduces the number of trainable parameters needed for adapting pre-trained models to new tasks. 3. **Regularization Techniques**: The paper investigates various regularization techniques, including weight and activation penalties, dropout placements, and additive Gaussian noise injection. 4. **Self-KAGNAttention Layers**: These layers enhance model performance, particularly in complex tasks. The authors conclude that KAN-based convolutional models can achieve state-of-the-art results in both classification and segmentation tasks, highlighting the effectiveness of Gram polynomials as the basis function and the advantages of scaling model width over depth. They also provide design principles for constructing successful KAN convolutional models and suggest future research directions, including refining these approaches and exploring additional regularization techniques.