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A Technical Critique of Some Parts of the Free Energy Principle

We summarize the original formulation of the free energy principle and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for and reveal, up to now unacknowledged, differences from newer f...

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Autores principales: Biehl, Martin, Pollock, Felix A., Kanai, Ryota
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997279/
https://www.ncbi.nlm.nih.gov/pubmed/33673663
http://dx.doi.org/10.3390/e23030293
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author Biehl, Martin
Pollock, Felix A.
Kanai, Ryota
author_facet Biehl, Martin
Pollock, Felix A.
Kanai, Ryota
author_sort Biehl, Martin
collection PubMed
description We summarize the original formulation of the free energy principle and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for and reveal, up to now unacknowledged, differences from newer formulations of the free energy principle. In particular, we reveal that various definitions of the “Markov blanket” proposed in different works are not equivalent. We show that crucial steps in the free energy argument, which involve rewriting the equations of motion of systems with Markov blankets, are not generally correct without additional (previously unstated) assumptions. We prove by counterexamples that the original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma, when it does hold, implies the equality of variational density and ergodic conditional density. The interpretation in terms of Bayesian inference hinges on this point, and we hence conclude that it is not sufficiently justified. Additionally, we highlight that the variational densities presented in newer formulations of the free energy principle and lemma are parametrised by different variables than in older works, leading to a substantially different interpretation of the theory. Note that we only highlight some specific problems in the discussed publications. These problems do not rule out conclusively that the general ideas behind the free energy principle are worth pursuing.
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spelling pubmed-79972792021-03-27 A Technical Critique of Some Parts of the Free Energy Principle Biehl, Martin Pollock, Felix A. Kanai, Ryota Entropy (Basel) Article We summarize the original formulation of the free energy principle and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for and reveal, up to now unacknowledged, differences from newer formulations of the free energy principle. In particular, we reveal that various definitions of the “Markov blanket” proposed in different works are not equivalent. We show that crucial steps in the free energy argument, which involve rewriting the equations of motion of systems with Markov blankets, are not generally correct without additional (previously unstated) assumptions. We prove by counterexamples that the original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma, when it does hold, implies the equality of variational density and ergodic conditional density. The interpretation in terms of Bayesian inference hinges on this point, and we hence conclude that it is not sufficiently justified. Additionally, we highlight that the variational densities presented in newer formulations of the free energy principle and lemma are parametrised by different variables than in older works, leading to a substantially different interpretation of the theory. Note that we only highlight some specific problems in the discussed publications. These problems do not rule out conclusively that the general ideas behind the free energy principle are worth pursuing. MDPI 2021-02-27 /pmc/articles/PMC7997279/ /pubmed/33673663 http://dx.doi.org/10.3390/e23030293 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 (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Biehl, Martin
Pollock, Felix A.
Kanai, Ryota
A Technical Critique of Some Parts of the Free Energy Principle
title A Technical Critique of Some Parts of the Free Energy Principle
title_full A Technical Critique of Some Parts of the Free Energy Principle
title_fullStr A Technical Critique of Some Parts of the Free Energy Principle
title_full_unstemmed A Technical Critique of Some Parts of the Free Energy Principle
title_short A Technical Critique of Some Parts of the Free Energy Principle
title_sort technical critique of some parts of the free energy principle
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997279/
https://www.ncbi.nlm.nih.gov/pubmed/33673663
http://dx.doi.org/10.3390/e23030293
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