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Exploring Simplicity Bias in 1D Dynamical Systems

Authors :
Kamal Dingle
Mohammad Alaskandarani
Boumediene Hamzi
Ard A. Louis
Source :
Entropy, Vol 26, Iss 5, p 426 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability–complexity relationships may be a useful tool when studying patterns in dynamical systems.

Details

Language :
English
ISSN :
10994300
Volume :
26
Issue :
5
Database :
Directory of Open Access Journals
Journal :
Entropy
Publication Type :
Academic Journal
Accession number :
edsdoj.390dc64a519e4cd0817c0f1cd07722aa
Document Type :
article
Full Text :
https://doi.org/10.3390/e26050426