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Memory and Markov Blankets
In theoretical biology, we are often interested in random dynamical systems—like the brain—that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biologic...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8469145/ https://www.ncbi.nlm.nih.gov/pubmed/34573730 http://dx.doi.org/10.3390/e23091105 |
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author | Parr, Thomas Da Costa, Lancelot Heins, Conor Ramstead, Maxwell James D. Friston, Karl J. |
author_facet | Parr, Thomas Da Costa, Lancelot Heins, Conor Ramstead, Maxwell James D. Friston, Karl J. |
author_sort | Parr, Thomas |
collection | PubMed |
description | In theoretical biology, we are often interested in random dynamical systems—like the brain—that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world—as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to ‘forget’ its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us. |
format | Online Article Text |
id | pubmed-8469145 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-84691452021-09-27 Memory and Markov Blankets Parr, Thomas Da Costa, Lancelot Heins, Conor Ramstead, Maxwell James D. Friston, Karl J. Entropy (Basel) Article In theoretical biology, we are often interested in random dynamical systems—like the brain—that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world—as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to ‘forget’ its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us. MDPI 2021-08-25 /pmc/articles/PMC8469145/ /pubmed/34573730 http://dx.doi.org/10.3390/e23091105 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Parr, Thomas Da Costa, Lancelot Heins, Conor Ramstead, Maxwell James D. Friston, Karl J. Memory and Markov Blankets |
title | Memory and Markov Blankets |
title_full | Memory and Markov Blankets |
title_fullStr | Memory and Markov Blankets |
title_full_unstemmed | Memory and Markov Blankets |
title_short | Memory and Markov Blankets |
title_sort | memory and markov blankets |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8469145/ https://www.ncbi.nlm.nih.gov/pubmed/34573730 http://dx.doi.org/10.3390/e23091105 |
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