Gaussian Process Kolmogorov-Arnold Networks
This work addresses the need for efficient and interpretable neural networks with built-in uncertainty quantification, primarily for machine learning practitioners, though it appears incremental as it extends existing KANs with probabilistic elements.
The paper tackles the problem of enhancing Kolmogorov-Arnold Networks (KANs) by integrating Gaussian Process (GP) neurons to enable probabilistic modeling and uncertainty estimation, resulting in a model with 80,000 parameters achieving 98.5% accuracy on MNIST classification, outperforming state-of-the-art models with 1.5 million parameters.
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.