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.
And it turns out that it is as doable systematically as extrapolation. For example, before reading the paper, can you guess an f(x,y) that is a simple reasonable generalization of this f(x)?
Hyperpolation
Link post
Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions
by Toby Ord
Abstract:
And it turns out that it is as doable systematically as extrapolation. For example, before reading the paper, can you guess an f(x,y) that is a simple reasonable generalization of this f(x)?