Gaussian Process Kolmogorov-Arnold Networks
<|reference_start|>Gaussian Process Kolmogorov-Arnold Networks: 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.<|reference_end|>
@article{chen2024gaussian,
    title={Gaussian Process Kolmogorov-Arnold Networks},
    author={Andrew Siyuan Chen},
    journal={arXiv preprint arXiv:2407.18397},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18397},
    primaryClass={cs.LG stat.ML}
}