Free-energy and the brain
Open accessAbstract
If one formulates Helmholtz's ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory input and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organisation and responses.In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure.
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A non-trivial property of life is its propensity to form multi-level and multi-scale structures of structures.
“This means that a non-trivial property of life is its propensity to form multi-level and multi-scale structures of structures [30].”
From The Markov blankets of life: autonomy, active inference and the free energy principle (2018) · cites this paper as [30]
In “The nature of biological systems,” the paper describes living systems as self-organising and able to preserve their physical structure. “Hierarchical dynamic models in the brain” describes organisation at multiple levels, but the paper does not establish the broader claim that life generally forms multi-level, multi-scale ‘structures of structures.’ Page numbers are unavailable in our copy. (LLM, conf=0.82)
Experimental — accuracy not yet measuredWithin the free-energy framework, average prediction error is captured by entropy, which quantifies an agent's informational cost for representing sensory input by its internal model.
“Within this framework, average prediction error is captured by the information theoretic measure entropy, which quanti fi es an agent ' s informational cost for representing the sensory input by its internal model.”
From Whatever next? Predictive brains, situated agents, and the future of cognitive science (2013) · cites this paper as Friston & Stephan 2007
In THEORY > A free-energy formulation (page unavailable), the paper describes an entropy term in information-theoretic free energy, and THEORY > The free-energy principle relates minimising free energy to minimising surprise. But it does not identify entropy as average prediction error or define it as an agent’s informational cost of representing sensory input; the entropy term is specifically the negative entropy of the ensemble density. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe free-energy principle states that all quantities that can change will change to minimize free-energy.
“The ' free-energy principle ' itself then states that ' all the quantities that can change; i.e. that are part of the system, will change to minimize free-energy ' (Friston & Stephan 2007, p. 427).”
From Whatever next? Predictive brains, situated agents, and the future of cognitive science (2013) · cites this paper as Friston & Stephan 2007
Hierarchical networks of neurons are thought to exchange top-down predictions and bottom-up prediction errors to achieve efficient information processing.
“hierarchical networks of neurons are thought to exchange top-down predictions and bottom-up prediction errors to achieve efficient information processing.”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [11]
The abstract variables of predictive models (predictions, prediction errors, precision weights) can be associated with specific neuron populations and connections in cortical microcircuits.
“The abstract variables of predictive models (predictions, prediction errors, precision weights) can be associated with specific neuron populations and connections in cortical microcircuits.”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [11]
Predictive coding hypotheses are testable with neurobiological data.
“These concrete mappings mean that predictive coding hypotheses are testable with neurobiological data (11).”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [11]
The predictive coding family provides a normative Bayesian account of perception and action in which the brain seeks to minimise surprise or free energy by aligning its internal model with the outside world.
“This family of frameworks provides a normative (Bayesian) account of perception and action, in which the brain seeks to minimise surprise or “free energy” by aligning its internal model with the outside world (11).”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [11]
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References 90 · Cited by 673
Research works printed but not linked: 5
- Haken H Synergistics: An introduction. Non-equilibrium phase transition and self-organisation in physics, chemistry and biology 1983 Springer Verlag Third Edition
- Kauffman S Self-organisation on selection in evolution 1993 Oxford University Press Oxford. UK
- MacKay DJC Free-energy minimisation algorithm for decoding and cryptoanalysis Electronics Letters 1995 31 445 447
- Nicolis G Prigogine I Self-organisation in non-equilibrium systems 1977 24 John Wiley New York, USA
- Nicolis G Prigogine I Self-organisation in non-equilibrium systems 1977 24 John Wiley New York, USA
- Authors
- Friston, K. J., & Stephan, K. E.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Friston, Karl J.
- Venue
- Synthese
- Published
- 2007-09-05
- Volume
- 159
- Issue
- 3
- Pages
- 417-458
- ISSN
- 0039-7857 (ISSN-L)
- 1573-0964
- PMC
- PMC2660582
- OpenAlex
- W2033613103
- Cited by
- 673
- References
- 90
- Citations by year
- 2026: 22 · 2025: 72 · 2024: 38 · 2023: 62 · 2022: 44 · 2021: 58 · 2020: 43 · 2019: 43 · 2018: 34 · 2017: 35 · 2016: 31 · 2015: 35 · 2014: 28 · 2013: 27 · 2012: 19
- FWCI
- 6.35
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Synthese (publishedVersion, cc-by-nc)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, other-oa)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Wellcome Trust (056750)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Embodied and Extended Cognition
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
- Keywords
- free energy principle, Helmholtz, perceptual inference, empirical Bayes, hierarchical models, prior expectations, surprise, perception and action, brain organization
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