Laurent Boué
2019 · arXiv
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.
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> 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
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 theoretical and physically-realizable models of computation is one of the weaknesses of the Chomsky hierarchy and classical approximation theory, and why more descriptive theories to characterize function complexity, e.g., circuit complexity, algebraic complexity theory and/or logical expressivity, are often needed. [1]: https://arxiv.org/pdf/1904.12320.pdf
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
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 areas they're not at all left-leaning, e.g.: Arvato, a division of the Bertelsmann Group, declared the privatization of public services a strategic business area. It should not surprise anyone that characterizing their politics on a one-dimensional left-right spectrum is inaccurate (findings such as https://arxiv.org/abs/1904.12320 notwithstanding).
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