## Memory and Markov Blankets

2021
##### Authors
Parr, Thomas
Da Costa, Lancelot
Friston, Karl J.
Journal article
Published
##### Published in
Entropy ; 23 (2021), 9. - 1105. - MDPI. - eISSN 1099-4300
##### Abstract
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.
##### Subject (DDC)
570 Biosciences, Biology
##### Keywords
Markov blanket; memory; conditional dependence; stochastic; density dynamics; Laplace assumption
##### Cite This
ISO 690PARR, Thomas, Lancelot DA COSTA, Conor HEINS, Maxwell James D. RAMSTEAD, Karl J. FRISTON, 2021. Memory and Markov Blankets. In: Entropy. MDPI. 23(9), 1105. eISSN 1099-4300. Available under: doi: 10.3390/e23091105
BibTex
@article{Parr2021-09Memor-54886,
year={2021},
doi={10.3390/e23091105},
title={Memory and Markov Blankets},
number={9},
volume={23},
journal={Entropy},
author={Parr, Thomas and Da Costa, Lancelot and Heins, Conor and Ramstead, Maxwell James D. and Friston, Karl J.},
note={Article Number: 1105}
}

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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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