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

TL;DR

This paper provides a comprehensive mathematical review of the free energy principle (FEP), analyzing its implementation, structure, and implications for understanding brain function in action and perception.

Contribution

It offers a detailed mathematical analysis of a biologically plausible FEP implementation, including a complete agent-based model and clarification of its assumptions.

Findings

Mathematical structure of FEP implementation elucidated

A simple agent-based model utilizing FEP is presented

Assumption structure of the FEP implementation is disclosed

Abstract

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