Real numbers, data science and chaos: How to fit any dataset with a single parameter

TL;DR

This paper demonstrates that any dataset, regardless of modality, can be approximated by a single-parameter scalar function using chaos theory principles, highlighting the expressive power of simple models.

Contribution

It introduces a method to fit any dataset with a single real parameter, expanding understanding of model expressiveness and generalization in data science.

Findings

Any dataset can be approximated by a single-parameter function.

The approach leverages chaos theory concepts for data fitting.

It broadens the perspective on model simplicity and expressiveness.

Abstract

We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos theory, we adopt a pedagogical approach demonstrating how to adjust this parameter in order to achieve arbitrary precision fit to all samples of the data. Targeting an audience of data scientists with a taste for the curious and unusual, the results presented here expand on previous similar observations regarding expressiveness power and generalization of machine learning models.