Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions

Fuente: arXiv
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Main Author: Ord, Toby
Format: Preprint
Published: 2024
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author Ord, Toby
author_facet Ord, Toby
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_05513
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions
Ord, Toby
Machine Learning
I.2.0
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.
title Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions
topic Machine Learning
I.2.0
url https://arxiv.org/abs/2409.05513