  In this paper, we introduce a probabilistic extension to Kolmogorov Arnold
Networks (KANs) by incorporating Gaussian Process (GP) as non-linear neurons,
which we refer to as GP-KAN. A fully analytical approach to handling the output
distribution of one GP as an input to another GP is achieved by considering the
function inner product of a GP function sample with the input distribution.
These GP neurons exhibit robust non-linear modelling capabilities while using
few parameters and can be easily and fully integrated in a feed-forward network
structure. They provide inherent uncertainty estimates to the model prediction
and can be trained directly on the log-likelihood objective function, without
needing variational lower bounds or approximations. In the context of MNIST
classification, a model based on GP-KAN of 80 thousand parameters achieved
98.5% prediction accuracy, compared to current state-of-the-art models with 1.5
million parameters.
