Real numbers, data science and chaos: How to fit any dataset with a single parameter
This work is incremental, expanding on previous observations about expressiveness and generalization in machine learning models.
The authors tackled the problem of fitting any dataset of any modality with a single real-valued parameter, achieving arbitrary precision fits to all samples using concepts from chaos theory.
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.