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Register a new userHigh--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality
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Alexander Gorban
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the curse of dimensionality states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the blessing of dimensionality, has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.
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This paper is the final part of the scientific discussion organised by the Journal Physics of Life Rviews about the simplicity revolution in neuroscience and AI. This discussion was initiated by the review paper The unreasonable effectiveness of small neural ensembles in high-dimensional brain. Phys Life Rev 2019, doi 10.1016/j.plrev.2018.09.005, arXiv:1809.07656. The topics of the discussion varied from the necessity to take into account the difference between the theoretical random distributions and extremely non-random real distributions and revise the common machine learning theory, to different forms of the curse of dimensionality and high-dimensional pitfalls in neuroscience. V. K{r{u}}rkov{a}, A. Tozzi and J.F. Peters, R. Quian Quiroga, P. Varona, R. Barrio, G. Kreiman, L. Fortuna, C. van Leeuwen, R. Quian Quiroga, and V. Kreinovich, A.N. Gorban, V.A. Makarov, and I.Y. Tyukin participated in the discussion. In this paper we analyse the symphony of opinions and the possible outcomes of the simplicity revolution for machine learning and neuroscience.
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