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The 'free energy principle' (FEP) has been suggested to provide a unifiedtheory of the brain, integrating data and theory relating to action,perception, and learning. The theory and implementation of the FEP combinesinsights from Helmholtzian 'perception as inference', machine learning theory,and statistical thermodynamics. Here, we provide a detailed mathematicalevaluation of a suggested biologically plausible implementation of the FEP thathas been widely used to develop the theory. Our objectives are (i) to describewithin a single article the mathematical structure of this implementation ofthe FEP; (ii) provide a simple but complete agent-based model utilising theFEP; (iii) disclose the assumption structure of this implementation of the FEPto help elucidate its significance for the brain sciences.

The free energy principle for action and perception: A mathematical review