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==Implications in biology==
In the context of biology to argue that the symmetries and modular arrangements observed in multiple species emerge from the tendency of evolution to prefer minimal Kolmogorov complexity.<ref>{{Cite journal |last1=Johnston |first1=Iain G. |last2=Dingle |first2=Kamaludin |last3=Greenbury |first3=Sam F. |last4=Camargo |first4=Chico Q. |last5=Doye |first5=Jonathan P. K. |last6=Ahnert |first6=Sebastian E. |last7=Louis |first7=Ard A. |date=2022-03-15 |title=Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution |journal=Proceedings of the National Academy of Sciences |volume=119 |issue=11 |pages=e2113883119 |doi=10.1073/pnas.2113883119 |doi-access=free |pmc=8931234 |pmid=35275794|bibcode=2022PNAS..11913883J }}</ref> Considering the genome as a program that must solve a task or implement a series of functions, shorter programs would be preferred on the basis that they are easier to find by the mechanisms of evolution.<ref>{{Cite journal |last=Alon |first=Uri |date=Mar 2007 |title=Simplicity in biology |url=https://www.nature.com/articles/446497a |journal=Nature |language=en |volume=446 |issue=7135 |pages=497 |doi=10.1038/446497a |pmid=17392770 |bibcode=2007Natur.446..497A |issn=1476-4687}}</ref> An example of this approach is the eight-fold symmetry of the compass circuit that is found across insect species, which correspond to the circuit that is both functional and requires the minimum Kolmogorov complexity to be generated from self-replicating units.<ref>{{Cite journal |last1=Vilimelis Aceituno |first1=Pau |last2=Dall'Osto |first2=Dominic |last3=Pisokas |first3=Ioannis |date=2024-05-30 |editor-last=Colgin |editor-first=Laura L |editor2-last=Vafidis |editor2-first=Pantelis |title=Theoretical principles explain the structure of the insect head direction circuit |url=https://elifesciences.org/articles/91533 |journal=eLife |volume=13 |pages=e91533 |doi=10.7554/eLife.91533 |doi-access=free |pmid=38814703 |issn=2050-084X}}</ref>
More broadly, the principles of Kolmogorov complexity have been extended beyond biology into computational modeling of natural systems. Hernández-Orozco et al. (2021) proposed an algorithmic [[loss function]] grounded in [[Algorithmic information theory]] to quantify the mismatch between predicted and observed system behavior. By integrating this approach with [[Machine learning]], they developed a framework for learning generative rules in non-differentiable and complex environments—bridging the gap between discrete algorithmic representations and continuous optimization.<ref>{{cite journal |last1=Zenil |first1=Hector |last2=Kiani |first2=Narsis A. |last3=Zea |first3=Allan A. |last4=Tegnér |first4=Jesper |title=Causal deconvolution by algorithmic generative models |journal=Nature Machine Intelligence |volume=1 |issue=1 |year=2019 |pages=58-66 |doi=10.1038/s42256-018-0005-0 }}</ref> This framework offers potential for uncovering underlying rules in both biological and artificial systems where structure and function co-evolve.<ref> {{cite book | last1=Zenil | first1=Hector | last2=Kiani | first2=Narsis A. | last3=Tegner | first3=Jesper | title=Algorithmic Information Dynamics: A Computational Approach to Causality with Applications to Living Systems | publisher=Cambridge University Press | year=2023 | doi=10.1017/9781108596619 | isbn=978-1-108-59661-9 | url=https://doi.org/10.1017/9781108596619}}</ref>
==Conditional versions==
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