LAWKI argues that the existence of a "Markov blanket" in an ergodic random dynamical system is sufficient for the internal coordinates \lambda of the Markov blanket to perform (or look like they perform) Bayesian inference on the external coordinates \psi. 2/n
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We identify technical problems that undermine LAWKI's justification for an interpretation as Bayesian inference. These problems only concern the relation between Markov blankets and Bayesian inference. They do not affect Friston's approach to constructing agents for a 3/n
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given environment/POMDP which is also called free energy principle or active inference. Instead of trying to construct an agent for a given environment LAWKI tries to give conditions for the existence of a Bayesian agent (and its environment) *inside* a given system. 4/n
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LAWKI: Existence of a Bayesian agent <=> internal coordinates \lamba of Markov blanket perform Bayesian inference on external coordinates \psi <=> \lambda parameterize pdist q(\psi|\lambda) that becomes equal to ergodic cond pdist p*(\psi|s,a,\lambda) due to system dynamics. 5/n
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We do not discuss these equivalences. We look at the arguments used in LAWKI to derive the last statement. These arguments contain technical errors. This means that LAWKI does not show that the Markov blanket is sufficient for a Bayesian agent. But maybe it is anyway... 6/n
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By now https://arxiv.org/pdf/1906.10184v1.pdf … (FEPP) and https://royalsocietypublishing.org/doi/full/10.1098/rsta.2019.0159 … appeared which argue the same for a different Bayesian agent notion. However, one error we identify in LAWKI is not entirely fixed in FEPP (see below). We do not know whether this is of consequence. 7/n
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What we show (fig): - first error: dropping relevant components of the gradient of the log of the ergodic pdist p* - second error: vanishing gradient of KL div does not imply equality of q and p* - alternative to first error: makes the Free Energy Lemma (FEL) impossible 8/npic.twitter.com/lJEdEv5vDI
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Also shown in the paper but not in the figure above: - FEPP alternative to first error also wrong - proof of FEL flawed - generalized coordinate version in https://ieeexplore.ieee.org/document/6767058 … also contains first error and a different but also flawed FEL proof 9/n
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We hope our will eventually lead to a clarification of these issues. Or at least to a revelation of the reasons for the newer formulations in FEPP and https://royalsocietypublishing.org/doi/full/10.1098/rsta.2019.0159 … No such reasons are given in these newer papers. 10/10
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Would you be willing to say that in general Friston tends to make bold claims but his arguments sometimes rely on complicated mathematic with little attention to formal proofs? Almost as if the proofs were either obvious or non-existent?
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