Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions
It addresses the problem of AI creativity for researchers, but is incremental as it builds on existing interpolation/extrapolation concepts.
The paper introduces hyperpolation as a method for generalizing to new dimensions outside the data's subspace, linking it to creativity in AI and suggesting current systems lack creativity due to limited hyperpolation ability.
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.