Convolutional Kolmogorov-Arnold Networks

The field of deep learning is constantly changing, the fast improvement of architectures has helped the advancement of computer vision in tasks involving complex spatial data. Convolutional Neural Networks proposed by LeCun et al.[5] are widely used due to their ability to handle high-dimensional data arrays such as images. Normally, these networks rely on linear transformations followed by an optional activation function in their convolutional layers to understand spatial relationships, which significantly reduced the number of parameters to capture complex patterns in images. In recent years, there has been an increase in the integration of advanced mathematical theories into deep learning architectures which have helped neural networks in handling complex data structures. Kolmogorov-Arnold Networks (KANs) [6] are a promising alternative to Multi-Layer Perceptrons (MLPs)[4] that use the Kolmogorov-Arnold theorem to integrate splines which is a key component of their architecture.