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A thread to comment on @danwilliamsphil’s preprint “Is the brain an organ for prediction error minimization?”
The preprint available here: http://philsci-archive.pitt.edu/18047/
Many sincere thanks to Dan for the pleasant and insightful exchanges that we've had about this paper. 1/20
The preprint available here: http://philsci-archive.pitt.edu/18047/
Many sincere thanks to Dan for the pleasant and insightful exchanges that we've had about this paper. 1/20
Before I begin criticizing the paper, I do want to emphasize that I’m a fan of Dan’s work. I think the paper benefits from being nicely written, very clear, and charitable. I think it makes some quite useful points. However, IMO, there are a few problems with the argument 2/20
Argument (p. 19):
P1. Any justification of prediction-error minimization (PEM) must bear on the causal relevance of prediction error minimization
P2. The free-energy principle (FEP) has no causal implications
C1. Therefore, the FEP does not provide any justification of PEM 3/20
P1. Any justification of prediction-error minimization (PEM) must bear on the causal relevance of prediction error minimization
P2. The free-energy principle (FEP) has no causal implications
C1. Therefore, the FEP does not provide any justification of PEM 3/20
I want to raise two objections.
First, IMO the paper mischaracterizes the FEP in ways that obscure its causal assumptions.
Second, IMO premise 2 is false. The FEP does make predictions about the causal structure of systems that minimize their variational free-energy. 4/20
First, IMO the paper mischaracterizes the FEP in ways that obscure its causal assumptions.
Second, IMO premise 2 is false. The FEP does make predictions about the causal structure of systems that minimize their variational free-energy. 4/20
First, core aspects of the FEP formalism aren’t considered.
Mathematically, the claim that FEP doesn’t make causal assumptions is a nonstarter. The dynamical formulation of Markov blankets is stipulatively defined in terms of causal dependencies, via the Langevin equation 5/20
Mathematically, the claim that FEP doesn’t make causal assumptions is a nonstarter. The dynamical formulation of Markov blankets is stipulatively defined in terms of causal dependencies, via the Langevin equation 5/20
In the paper, the FEP is equated with the claim that systems maintain themselves away from equilibrium by minimizing free-energy. Although there’s some discussion of this process as variational inference, this formulation obscures the causal assumptions of the FEP. 6/20
The FEP per se is the statement that if a system exists that has a Markov blanket (MB) and a nonequilibrium steady state (NESS) density and mixes weakly with its environment, then we can associate its internal states with probability densities or beliefs over external states 7/20
More precisely, the FEP says that for every blanket state of a system, we can define an average of internal states that we can interpret as the sufficient statistics (e.g., mean or variance) of Bayesian beliefs about fictive external states. That is the core of the FEP. 8/20
The dynamical Markov or Friston blankets are quintessentially causal, as are the dynamics that underwrite them – and the FEP justifies PEM as a process theory, since PEM is derived mathematically from the FEP. (Dan doesn’t deny that PEM can be derived formally from the FEP) 9/20
This focus on technical detail matters because it leads to the process theory, active inference, being mischaracterized in the paper. It isn’t the case that free-energy needs to be computed explicitly by the system. We’ve argued this at length here: https://journals.sagepub.com/doi/full/10.1177/1059712319862774 10/20
What the FEP says is that the trajectory of the system through state space is also a trajectory through a statistical manifold, where the coordinates of that manifold are the parameters of beliefs about fictive external states. The free-energy is implicit in the dynamics 11/20
What is really at play is constraints on the flow of certain quantities: that the flow behave as if these variables parameterized beliefs. The free-energy only exists to derive the flow of states. It does not need to be explicitly computed and represented by the system. 12/20
So much for the first point.
RE: my claim that premise 2 is false, I point to two counterexamples.
First, since the MB formalismis recursively applied under FEP, FEP predicts that free-energy minimizing systems will be structured as nested Markovian systems (of systems) 13/20
RE: my claim that premise 2 is false, I point to two counterexamples.
First, since the MB formalismis recursively applied under FEP, FEP predicts that free-energy minimizing systems will be structured as nested Markovian systems (of systems) 13/20
This is a prediction about the causal structure of free-energy minimizing systems that is derived directly from the FEP formalism. It is predicted for brains here ( https://arxiv.org/abs/2006.02741 ) and borne out empirically in "Parcels and particles," here ( https://arxiv.org/abs/2007.09704 ) 14/20
Another causal prediction specific to FEP is that all living systems should have a NESS density. E.g., Studies of (e.g.) cancer genesis using Markovian methods to separate internal states from external ones support this assumption https://pubmed.ncbi.nlm.nih.gov/28212112/ 15/20
The assumption that the system’s state space has an underlying NESS density is supported also by work on early myelopoiesis in real biological systems. Core molecular endogenous networks in this study were modeled using dynamical equations, see https://pubmed.ncbi.nlm.nih.gov/28646471/ 16/20
N.B. These are theoretical predictions about the specific causal structure of free-energy minimizing systems that follow directed from the FEP formalism: the nested Markovian structure and presence of NESS density are predictions of FEP and counterexamples to premise 2. 17/20
In closing, I want grant some of Dan’s points. First, the claim that brain’s exclusive function is to minimize prediction error is probably wrong. I think that’s because PEM isn’t a function of the brain, but rather the mechanism by which any brain function is realized. 18/20
Second, Dan’s paper discusses an often-overlooked aspect of the FEP: It is a principle from which several different process theories (like predictive coding and active inference) can be derived. We gain clarity by realizing that process theories are under-determined by FEP 19/20
In sum, the paper is beautifully written, but its formulation of the FEP obscures its causal assumptions, and premise 2 of its argument is false. But it makes some interesting points and raises some interesting issues. Many thanks to Dan for the opportunity for dialogue. 20/20
