The free-energy principle: a rough guide to the brain?

doi:10.1016/j.tics.2009.04.005

Trends in Cognitive Sciences

Volume 13, Issue 7, July 2009, Pages 293-301

https://doi.org/10.1016/j.tics.2009.04.005 Get rights and content

This article reviews a free-energy formulation that advances Helmholtz's agenda to find principles of brain function based on conservation laws and neuronal energy. It rests on advances in statistical physics, theoretical biology and machine learning to explain a remarkable range of facts about brain structure and function. We could have just scratched the surface of what this formulation offers; for example, it is becoming clear that the Bayesian brain is just one facet of the free-energy principle and that perception is an inevitable consequence of active exchange with the environment. Furthermore, one can see easily how constructs like memory, attention, value, reinforcement and salience might disclose their simple relationships within this framework.

Introduction

The free-energy (see Glossary) principle is a simple postulate with complicated implications. It says that any adaptive change in the brain will minimize free-energy. This minimisation could be over evolutionary time (during natural selection) or milliseconds (during perceptual synthesis). In fact, the principle applies to any biological system that resists a tendency to disorder; from single-cell organisms to social networks.

The free-energy principle is an attempt to explain the structure and function of the brain, starting from the very fact that we exist: this fact places constraints on our interactions with the world, which have been studied for years in evolutionary biology and systems theory. However, recent advances in statistical physics and machine learning point to a simple scheme that enables biological systems to comply with these constraints. If one looks at the brain as implementing this scheme (minimising a variational bound on disorder), nearly every aspect of its anatomy and physiology starts to make sense. What follows is a review of this new perspective on old ideas.

Section snippets

Free-energy and self-organization

So what is free-energy? Free-energy is an information theory quantity that bounds the evidence for a model of data 1, 2, 3. Here, the data are sensory inputs and the model is encoded by the brain. More precisely, free-energy is greater than the negative log-evidence or ‘surprise’ in sensory data, given a model of how they were generated. Crucially, unlike surprise itself, free-energy can be evaluated because it is a function of sensory data and brain states. In fact, under simplifying

New perspectives?

We have tried to substantiate the aforementioned formulation by explaining many empirical aspects of anatomy and physiology in terms of optimising free-energy. One can explain a remarkable range of facts; for example, the hierarchical arrangement of cortical areas, functional asymmetries between forward and backward connections, explaining away effects and many psychophysical and cognitive phenomena; see Ref. [19] and Table 1. However, we now focus on prospective issues that could offer new and

Conclusion

In conclusion, the free-energy principle might provide a comprehensive account of how we represent the world and come to sample it adaptively. Furthermore, it provides a mathematical specification of ‘what’ the brain is doing; it is suppressing free-energy. If this uses gradient descent, one can derive differential equations that prescribe recognition dynamics that specify ‘how’ the brain might operate. The ensuing representations are used to elaborate prediction errors, which action tries to

Acknowledgements

The Wellcome Trust funded this work. I would like to thank my colleagues at the Wellcome trust Centre for Neuroimaging and the Gatsby Computational Neuroscience unit for helpful and formative discussions.

Glossary

[Kullback-Leibler] divergence: information divergence, information gain, cross or relative entropy is a non-commutative measure of the difference between two probability distributions.
Bayesian surprise: a measure of salience based on the divergence between the recognition and prior densities. It measures the information in the data that can be recognised.
Conditional density: or posterior density is the probability distribution of causes or model parameters, given some data; i.e., a probabilistic

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Trends in Cognitive Sciences

OpinionThe free-energy principle: a rough guide to the brain?

Introduction

Section snippets

Free-energy and self-organization

New perspectives?

Conclusion

Acknowledgements

Glossary

J. Physiol. Paris

Trends Neurosci.

Neuron

J. Physiol. Paris

Trends Cogn. Sci.

Curr. Opin. Neurobiol.

Neuroimage

Trends Neurosci.

Neural Netw.

Trends Cogn. Sci.

Curr. Opin. Neurobiol.

Neuron

Brain Res.

Neuron.

Neuroscience

Neural Netw.

Statistical Mechanics

Free-energy minimisation algorithm for decoding and cryptoanalysis

Electron. Lett.

A view of the EM algorithm that justifies incremental, sparse, and other variants

Parallel visual computation

Nature

The Helmholtz machine

Neural Comput.

Hierarchical Bayesian inference in the visual cortex

J. Opt. Soc. Am. A. Opt. Image Sci. Vis

Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive field effects

Nat. Neurosci.

A theory of cortical responses

Philos. Trans. R. Soc. Lond. B Biol. Sci.

Free energy and the brain

Synthese

Synaptic depression and cortical gain control

Science

A neural substrate of prediction and reward

Science

Opinion
The free-energy principle: a rough guide to the brain?