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The math is not the territory: navigating the free energy principle

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Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”

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  1.  For a thorough overview of the FEP/MaxEnt connection, refer to Gottwald and Braun 2020.

  2.  We may think of the Hamiltonian of a physical system as the net kinetic and potential energies of all of the particles in the system.

  3.  Friston notes that it is interesting that the formulation of free energy minimisation using gradient flows (otherwise known as gradient descent) was an important practical development for the data analysis tools commonly applied in neuroscience—for example, in dynamic causal modelling. In brief, this freed one from the analytic derivations of vanilla variational Bayes and the use of conjugate priors; enabling a generic variational scheme for modelling empirical data known as variational Laplace.


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This paper has benefited tremendously from thoughtful feedback and lengthy discussions with many people, most notably Liam Bright, Tony Chemero, Andrew Corcoran, Carolyn Dicey Jennings and the Philosophy Lab at UC Merced, Krzysztof Dołega, Thomas van Es, Karl Friston, Cecilia Heyes, Bryce Huebner, Alex Kiefer, Michael Kirchhoff, Maxwell Ramstead, and Dalton Sakthivadivel.

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Andrews, M. The math is not the territory: navigating the free energy principle. Biol Philos 36, 30 (2021).

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