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

arXiv: https://arxiv.org/abs/1705.09156 · HTML: https://mlsanity.com/paper/1705.09156/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2017.

## Built on by (most cited first, 30 of 66)

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- [Applications of the Free Energy Principle to Machine Learning and Neuroscience](https://mlsanity.com/paper/2107.00140/) (2021)
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## Abstract (arXiv)

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.