Thanks, very interesting discussion! Let me add some additional concerns pertaining to FEP theory:
Markov blankets, to the best of my knowledge, have never been derived, either precisely or approximately, for physical systems. Meanwhile, they play the key role in all subsequent derivations in FEP. Markov blankets don’t seem to me as fundamental as entropy, free energy, etc., to be just postulated. Or, if they are introduced as an assumption, it would be worthwhile to affirm that this assumption is feasible for the real-world systems, justifying their key role in the theory.
The Helmholtz-Ao decomposition refers to the leading term in the series expansion in terms of σ (or the effective noise temperature T) as a small parameter. Consequently, subsequent equations in FEP are exact only at the potential function’s global minimum. In other words, we can’t make any exact conclusions about the states of the brain or the environment, except for the only state with the highest probability density at steady state. Perhaps adding higher-order terms (in σ or T) to the Helmholtz-Ao decomposition could fix this, but I’ve never seen such attempts in FEP papers.
Also, a nice review by Millidge, Seth, Buckley (2021) lists several dozens of assumptions required for FEP. The assumption I find most problematic is that the environment is presumed to be at steady state. This appears intuitively at odds with the biological scenarios of the emergence of the nervous system and the human brain.
> Markov blankets, to the best of my knowledge, have never been derived, either precisely or approximately, for physical systems
This paper does just that. It introduces a ‘blanket index’ by which any state space can be analyzed to see whether a markov blanket assumption is suitable or not. Quoting MJD Ramstead’s summary of the paper’s results with respect to the markov blanket assumption:
We now know that, in the limit of increasing dimensionality, essentially all systems (both linear and nonlinear) will have Markov blankets, in the appropriate sense. That is, as both linear and nonlinear systems become increasingly high-dimensional, the probability of finding a Markov blanket between subsets approaches 1.
The assumption I find most problematic is that the environment is presumed to be at steady state
Note the assumption is that the environment is at a nonequilibrium steady state, not a heat-death-of-the-universe steady state. My reading of this is that it is an explicit assumption that probabilistic inference is possible.
Thanks, very interesting discussion! Let me add some additional concerns pertaining to FEP theory:
Markov blankets, to the best of my knowledge, have never been derived, either precisely or approximately, for physical systems. Meanwhile, they play the key role in all subsequent derivations in FEP. Markov blankets don’t seem to me as fundamental as entropy, free energy, etc., to be just postulated. Or, if they are introduced as an assumption, it would be worthwhile to affirm that this assumption is feasible for the real-world systems, justifying their key role in the theory.
The Helmholtz-Ao decomposition refers to the leading term in the series expansion in terms of σ (or the effective noise temperature T) as a small parameter. Consequently, subsequent equations in FEP are exact only at the potential function’s global minimum. In other words, we can’t make any exact conclusions about the states of the brain or the environment, except for the only state with the highest probability density at steady state. Perhaps adding higher-order terms (in σ or T) to the Helmholtz-Ao decomposition could fix this, but I’ve never seen such attempts in FEP papers.
Also, a nice review by Millidge, Seth, Buckley (2021) lists several dozens of assumptions required for FEP. The assumption I find most problematic is that the environment is presumed to be at steady state. This appears intuitively at odds with the biological scenarios of the emergence of the nervous system and the human brain.
This paper does just that. It introduces a ‘blanket index’ by which any state space can be analyzed to see whether a markov blanket assumption is suitable or not. Quoting MJD Ramstead’s summary of the paper’s results with respect to the markov blanket assumption:
Note the assumption is that the environment is at a nonequilibrium steady state, not a heat-death-of-the-universe steady state. My reading of this is that it is an explicit assumption that probabilistic inference is possible.