HackerPapers

arXiv:1904.12320cs.LG

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

Laurent Boué

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.

arXiv comments
Journal reference
DOI
Subjects
cs.LGMachine Learning cs.DMDiscrete Mathematics cs.IRInformation Retrieval stat.MLMachine Learning (Statistics)

On Hacker News

Linked by 4 identifiable commenters in 4 comments across 4 threads, from May 2019 to Apr 2023. Found in 4 HN submissions from May 2019 to Sep 2021. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments4 threads

  1. Tighter bounds on the expressivity of transformer encoders 1 comment

    • With arbitrary-precision, you can essentially replace the entire neural network with a single trainable parameter. [1] Likewise, in model checking, one often uses bounded-length bitvectors, because even a PDA with two stacks is Turing-equivalent. The poor separability between…

      bmc7505View on HNParent context

  2. How to fit any dataset with a single parameter 1 comment

    • This is a very interesting idea, even if not really practical. The author has more details in the paper: https://arxiv.org/abs/1904.12320

      vladohView on HNParent context

  3. At Axel Springer, Politico’s New Owner, Allegations of Sex, Lies, Secret Payment 1 comment

    • The Bertelsmann Foundation wants to promote social integration and diversity. It advocates for creating a "comprehensive and long-term migration architecture" for Germany. - https://en.wikipedia.org/wiki/Bertelsmann_Stiftung#Society But as the sibling comment notes, in other…

      chuckeeView on HNParent context

  4. Why are 2D vector graphics so much harder than 3D? 1 comment

    • > For any arbitrarily complex curve, I think I can give you a 1D parameterization for it. If you haven't see it already, read this paper by Laurent Boue: "Real numbers, data science and chaos: How to fit any dataset with a single parameter" https://arxiv.org/abs/1904.12320

      stevesimmonsView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.