Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview

Version 1 : Received: 16 March 2021 / Approved: 16 March 2021 / Online: 16 March 2021 (09:46:20 CET)

A peer-reviewed article of this Preprint also exists.

Kreinovich, V.; Kosheleva, O. Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview. Entropy 2021, 23, 501. Kreinovich, V.; Kosheleva, O. Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview. Entropy 2021, 23, 501.

Journal reference: Entropy 2021, 23, 501
DOI: 10.3390/e23050501

## Abstract

As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system’s complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution get close to an easy-to-analyze normal one – and indeed, normal distributions are ubiquitous. We show that such limit theorems make analysis of complex systems easier – i.e., lead to blessing of dimensionality phenomenon – for all the aspects of these systems: the corresponding transformation, the system’s uncertainty, and the desired result of the system’s analysis.

## Keywords

limit theorems; curse and blessing of dimensionality; neural networks

## Subject

MATHEMATICS & COMPUTER SCIENCE, General & Theoretical Computer Science

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