A technical critique of the free energy principle as presented in "Life as we know it" and related works

We summarize the argument in Friston (2013, this https URL) and highlight some technical errors. We also discuss how these errors affect the very similar Friston (2014, this https URL) and, where appropriate, mention consequences for the newer proposals in Friston (2019, arXiv:1906.10184v1 ) and Parr et al. (2019, this https 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.