We summarize the argument in Friston (2013, URL and highlight some technical errors. We also discuss how these errors affect the  similar Friston (2014, URL  The errors call into question the purported interpretation that the internal coordinates of every system with a Markov blanket will appear to engage in Bayesian inference. In particular,  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 equivalent . 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 , arXiv:1906.10184v1 ). The second error is the lack of a proof of the existence of the free energy as claimed by the Free Energy Lemma  . The third is the assumption that a non-negative function whose gradient vanishes at some point necessarily has a minimum at that point and that its value at this minimum is zero. However, if the function is constant, which is the case here, its gradient vanishes everywhere, it has no minimum at any point, and its value can be arbitrarily large . The interpretation in terms of Bayesian inference hinges on this point, and we hence conclude that it is unjustified  .
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 blanket will 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 wrong in 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 .
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very
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and, where appropriate, mention consequences for the newer proposals in Friston (2019, arXiv:1906.10184v1 ) and Parr et al. (2019, URL
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in addition to highlighting the implicit restriction to linear models,
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equivalent
generally correct
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, arXiv:1906.10184v1
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is the lack of a proof of the existence of the free energy as claimed by the
concerns the
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itself, which we prove, by counterexample, to be wrong in general
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assumption that a non-negative function whose gradient vanishes at some point necessarily has a minimum at that point and that its value at this minimum is zero. However, if the function is constant, which is the case here, its gradient vanishes everywhere, it has no minimum at any point, and its value can be arbitrarily large
claim that the Free Energy Lemma, when it does hold, implies equality of variational density and ergodic conditional density
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. 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