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A Technical Critique of Some Parts of the Free Energy Principle

by 1,*,†, 2,*,† and 1
1
Araya Inc., Tokyo 107-6024, Japan
2
School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Australia
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Kevin H. Knuth
Entropy 2021, 23(3), 293; https://doi.org/10.3390/e23030293
Received: 16 September 2020 / Revised: 19 December 2020 / Accepted: 24 February 2021 / Published: 27 February 2021
(This article belongs to the Section Entropy and Biology)
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. View Full-Text
Keywords: free energy principle; stochastic differential equations; Markov blanket free energy principle; stochastic differential equations; Markov blanket
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MDPI and ACS Style

Biehl, M.; Pollock, F.A.; Kanai, R. A Technical Critique of Some Parts of the Free Energy Principle. Entropy 2021, 23, 293. https://doi.org/10.3390/e23030293

AMA Style

Biehl M, Pollock FA, Kanai R. A Technical Critique of Some Parts of the Free Energy Principle. Entropy. 2021; 23(3):293. https://doi.org/10.3390/e23030293

Chicago/Turabian Style

Biehl, Martin, Felix A. Pollock, and Ryota Kanai. 2021. "A Technical Critique of Some Parts of the Free Energy Principle" Entropy 23, no. 3: 293. https://doi.org/10.3390/e23030293

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