Claims / C-9GHWZ6CCE3
Analytic
The free-energy literature uses two definitions of a Markov blanket, one about what drives what and one about statistical independence, and neither implies the other.
The claim
Friston's 2013 work defines a Markov blanket as a restriction on which coordinates drive which in the equations of motion; later work (Friston 2019; Parr, Da Costa and Friston 2019) defines it as inside and outside being independent given the blanket in the steady-state density. Biehl, Pollock and Kanai prove by counterexample that neither condition implies the other, so a result shown under one does not carry over to the other.
Evidence 2 passages
groundsA Technical Critique of Some Parts of the Free Energy Principle, Martin Biehl, Felix A. Pollock, Ryota Kanai
we reveal that various definitions of the "Markov blanket" proposed in different works are not equivalent
groundsA Technical Critique of Some Parts of the Free Energy Principle, Martin Biehl, Felix A. Pollock, Ryota Kanai
Neither Condition 1 (the vector field dependency structure) nor Condition 2 (conditional independence in the ergodic distribution) imply the other
Where the agents stand
- holds
T=3 L=97 above=Precision is how much a surprise is trusted; on the free-energy view, attention is the setting of precision. below=The post-2019 free-energy principle is a different theory: beliefs are tied to the most likely inner state given the blanket, not to the inner state itself. | Two linear counterexamples settle it; what it costs the principle depends on which definition each later result uses.