We summarize the argument in Friston (2013, URL and highlight some technical errors. We also discuss how these errors affect the very similar Friston (2014, URL and, where appropriate, mention consequences for the newer proposals in Friston (2019, arXiv:1906.10184v1 ) and Parr et al. (2019, URL The errors call into question the purported interpretation that the internal coordinates of every system with a Markov blanketwill appear to engage in Bayesian inference. In particular, in addition to highlighting the implicit restriction to linear models, we identify three formal errors in the main argument of Friston (2013): The first concerns the rewriting of the  equations of motion of systems with Markov blankets which turns out not to be generally correct . We prove  the non-equivalence with a counterexample that exhibits a Markov blanket but does not satisfy the rewritten equations. Our counterexample also invalidates the corresponding (but more general) rewritten equations in the more recent Friston (2019). The second error concerns the Free Energy Lemma itself, which we prove, by counterexample, to be wrongin general. The third is the claim that the Free Energy Lemma , when it does hold, implies 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 unjustified . Additionally, we highlight that the definitions of the Markov blanket in Friston (2013) and Parr et al. (2019) are not equivalent and that the assumptions in Parr et al. (2019) may be too strong to allow for meaningful interpretation .
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 to 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 counterexample 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 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 parameterised 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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argument in Friston (2013, URL
original formulation of the free energy principle,
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errors. We also
issues. We
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errors affect the very similar Friston (2014, URL
issues affect related results involving generalised coordinates
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the newer proposals in Friston (2019, arXiv:1906.10184v1 ) and Parr et al. (2019, URL The errors call into question the purported interpretation that the internal coordinates of every system with a Markov blanketwill appear to engage in Bayesian inference. In particular, in addition to highlighting the implicit restriction to linear models, we identify three formal errors in the main argument of Friston (2013): The first concerns the rewriting of
and reveal, up to now unacknowledged, differences to newer formulations of the free energy principle. In particular, we reveal that various definitions of
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"Markov blanket" proposed in different works are not equivalent. We show that crucial steps in the free energy argument which involve rewriting the
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which turns out not to be generally correct
, are not generally correct without additional (previously unstated) assumptions
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by counterexample that
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non-equivalence with a counterexample that exhibits a Markov blanket but does not satisfy the rewritten equations. Our counterexample also invalidates the corresponding (but more general) rewritten equations in the more recent Friston (2019). The second error concerns the Free Energy Lemma itself, which we prove, by counterexample, to be wrongin general. The third is the claim that the Free Energy Lemma
original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma
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unjustified
not sufficiently justified
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definitions of the Markov blanket in Friston (2013) and Parr et al. (2019) are not equivalent and that the assumptions in Parr et al. (2019) may be too strong to allow for meaningful interpretation
variational densities presented in newer formulations of the free energy principle and lemma are parameterised 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