Exploring simplicity bias in 1D dynamical systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911873967849472 |
|---|---|
| author | Dingle, Kamaludin Alaskandarani, Mohammad Hamzi, Boumediene Louis, Ard A. |
| author_facet | Dingle, Kamaludin Alaskandarani, Mohammad Hamzi, Boumediene Louis, Ard A. |
| contents | 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 \emph{simplicity bias}. By viewing the parameters of dynamical systems as inputs, and 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 output pattern probability is used to make \emph{a priori} predictions for 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 in studying patterns in dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring simplicity bias in 1D dynamical systems Dingle, Kamaludin Alaskandarani, Mohammad Hamzi, Boumediene Louis, Ard A. Dynamical Systems Adaptation and Self-Organizing Systems 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 \emph{simplicity bias}. By viewing the parameters of dynamical systems as inputs, and 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 output pattern probability is used to make \emph{a priori} predictions for 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 in studying patterns in dynamical systems. |
| title | Exploring simplicity bias in 1D dynamical systems |
| topic | Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2403.06989 |