Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions
<|reference_start|>Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions: This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value of a function at new locations that lie outside the subspace (or manifold) of the existing data. We shall see that hyperpolation is possible and explore its links to creativity in the arts and sciences. We will also examine the role of hyperpolation in machine learning and suggest that the lack of fundamental creativity in current AI systems is deeply connected to their limited ability to hyperpolate.<|reference_end|>
@article{ord2024interpolation,,
    title={Interpolation, Extrapolation, Hyperpolation: Generalising into new
  dimensions},
    author={Toby Ord},
    journal={arXiv preprint arXiv:2409.05513},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05513},
    primaryClass={cs.LG}
}