Probabilistic Kolmogorov-Arnold Networks via Sparsified Deep Gaussian Processes with Additive Kernels

In this paper, we propose a new probabilistic formulation of the Kolmogorov-Arnold neural network model with the sparsity constraint. To achieve this, we first prove that replacing the edge of the KAN model by the Gaussian process is equivalent to a deep Gaussian Process model with additive kernel structure. To achieve a similar sparse network architecture like the KAN model, we incorporate the spike and slab prior distribution to the proposed model to learn the sparse network structure, aiming at reducing unnecessary network parameters while keeping the model accuracy unchanged. In addition, an efficient variational inference algorithm is proposed and validated in a simulation study and some benchmark datasets.