  The emergence of Kolmogorov-Arnold Networks (KANs) has sparked significant
interest and debate within the scientific community. This paper explores the
application of KANs in the domain of computer vision (CV). We examine the
convolutional version of KANs, considering various nonlinearity options beyond
splines, such as Wavelet transforms and a range of polynomials. We propose a
parameter-efficient design for Kolmogorov-Arnold convolutional layers and a
parameter-efficient finetuning algorithm for pre-trained KAN models, as well as
KAN convolutional versions of self-attention and focal modulation layers. We
provide empirical evaluations conducted on MNIST, CIFAR10, CIFAR100, Tiny
ImageNet, ImageNet1k, and HAM10000 datasets for image classification tasks.
Additionally, we explore segmentation tasks, proposing U-Net-like architectures
with KAN convolutions, and achieving state-of-the-art results on BUSI, GlaS,
and CVC datasets. We summarized all of our findings in a preliminary design
guide of KAN convolutional models for computer vision tasks. Furthermore, we
investigate regularization techniques for KANs. All experimental code and
implementations of convolutional layers and models, pre-trained on ImageNet1k
weights are available on GitHub via this
https://github.com/IvanDrokin/torch-conv-kan
