# Interpolation, Extrapolation, Hyperpolation: Generalising into new dimensions

arXiv: https://arxiv.org/abs/2409.05513 · HTML: https://mlsanity.com/paper/2409.05513/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 1 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 1 of 1)

- [VASA-1: Lifelike Audio-Driven Talking Faces Generated in Real Time](https://mlsanity.com/paper/2404.10667/) (2024)

## Built on by (most cited first, 1 of 1)

- [On the Creativity of AI Agents](https://mlsanity.com/paper/2604.13242/) (2026)

## Abstract (arXiv)

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.