Active inference: a process theory
Open accessAbstract
This article describes a process theory based on active inference and belief propagation. Starting from the premise that all neuronal processing (and action selection) can be explained by maximizing Bayesian model evidence—or minimizing variational free energy—we ask whether neuronal responses can be described as a gradient descent on variational free energy. Using a standard (Markov decision process) generative model, we derive the neuronal dynamics implicit in this description and reproduce a remarkable range of well-characterized neuronal phenomena. These include repetition suppression, mismatch negativity, violation responses, place-cell activity, phase precession, theta sequences, theta-gamma coupling, evidence accumulation, race-to-bound dynamics, and transfer of dopamine responses. Furthermore, the (approximately Bayes’ optimal) behavior prescribed by these dynamics has a degree of face validity, providing a formal explanation for reward seeking, context learning, and epistemic foraging. Technically, the fact that a gradient descent appears to be a valid description of neuronal activity means that variational free energy is a Lyapunov function for neuronal dynamics, which therefore conform to Hamilton’s principle of least action.
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The perception-action cycle and active inference make evaluation emergent from the agent's ongoing interaction with the environment, arising either through optimization of information flow or through minimization of expected surprise.
“The perception-action cycle (Tishby and Polani, 2010) and active inference (Friston et al., 2017) both make evaluation emergent from the agent's ongoing interaction with the environment, arising either through optimization of information flow or through minimization of expected surprise.”
From Toward Enactive Artificial Intelligence (2026) · cites this paper as Friston et al., 2017
Sections 2.2 and 2.8 describe a continuing perception–action cycle in which new observations inform the evaluation of policies. Section 2.3 says policies minimize expected free energy, not simply expected surprise; it also says epistemic value can maximize expected Bayesian surprise. The information-flow alternative is attached to the other citation, not this one. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe marginal likelihood term scores the plausibility of a particle pursuing a path and is usually interpreted in terms of expected loss and pragmatic affordance.
“This marginal likelihood scores the plausibility of a particle pursuing this kind of path and is usually interpreted in terms of expected loss (i.e., negative expected reward or utility) [66, 63], and pragmatic affordance [153, 123].”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [123]
Section 2.3 links the expected free energy of a policy to expected cost, utility, and pragmatic or extrinsic value, supporting the pragmatic interpretation. It does not describe a particle pursuing a path or say that a marginal-likelihood term scores the plausibility of that path; those specifics are not supported by this source. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe brain builds a generative model of the world, constantly explaining its observations (active inference).
“A prevailing account of human perception is that the brain builds a generative model of the world, constantly explaining its observations (Friston et al., 2017), i.e. active inference.”
From Object-Centric Scene Representations Using Active Inference (2024) · cites this paper as Friston et al., 2017
These beliefs are used to evaluate the expected free energy of allowable policies, from which actions can be selected.
“These beliefs are then used to evaluate the expected free energy of allowable policies, from which actions can be selected [123, 124, 125].”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [123]
The conditional independencies among states implicit in partially observed Markov decision processes entail the functional forms for variational and expected free energies.
“The conditional independencies among states implicit in partially observed Markov decision processes entail the above functional forms for variational and expected free energies [124, 123].”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [123]
The ensuing minimisation of free energy can be formulated as gradient flows between discrete arrivals of new sensory input, relating comfortably to neuronal dynamics.
“The ensuing minimisation of free energy can be formulated as gradient flows following (17)—between the discrete arrival of new sensory input—in a way that relates comfortably to neuronal dynamics [123, 124, 42].”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [123]
AI-C can similarly be described as presenting a predictive processing account of conscious experience; however, unlike NREP, it is specifically committed to the process theory developed under the free energy principle.
“AI-C can similarly be described as presenting a predictive processing account of conscious experience; however, unlike NREP, it is specifically committed to the process theory developed under the free energy principle (Friston et al., 2017; Parr et al., 2022) -with the caveat that the precise implementational details described at the process theory level are themselves subject to development (e.g.”
From Integrated information and predictive processing theories of consciousness: An adversarial collaborative review (2026) · cites this paper as Friston et al., 2017
The free-energy principle implies that organisms can minimise uncertainty through action, actively sampling the environment to reduce ambiguity and confirm or disconfirm their predictions, as formalised under active inference.
“it also implies that organisms can minimise uncertainty through action, actively sampling the environment to reduce ambiguity and confirm or disconfirm their predictions, as formalised under active inference (17).”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [17]
Under active inference, actions are selected to minimise expected free energy, reducing uncertainty and maintaining preferred states.
“Under active inference, actions are selected to minimise expected free energy, reducing uncertainty and maintaining preferred states (17).”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [17]
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Self-citationPrecision and neuronal dynamics in the human posterior parietal cortex during evidence accumulation
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Self-citationSelection of cortical dynamics for motor behaviour by the basal ganglia
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Self-citationActive Inference, Curiosity and Insight
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Self-citationInterpreting and Utilising Intersubject Variability in Brain Function
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Self-citationUncertainty, epistemics and active inference
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Self-citationComputational mechanisms of curiosity and goal-directed exploration
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Self-citationA step-by-step tutorial on active inference and its application to empirical data
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Self-citationDeeply Felt Affect: The Emergence of Valence in Deep Active Inference
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Generalised free energy and active inference
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Self-citationA tale of two densities: active inference is enactive inference
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Self-citationActive inference on discrete state-spaces: A synthesis
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“For the purpose of this paper we use a particular (structured) mean-field approximation (c.f., Figure 2): This choice is driven by didactic purposes and since this factorisation has been used extensively in the active inference literature (e.g., [2, 27, 43]).”
BackgroundMethodResultInfluentialSelf-citationWorking memory, attention, and salience in active inference
Parr, T., & Friston, K. J. (2017) · Scientific Reports · doi:10.1038/s41598-017-15249-0 · Cited by 226 · see citing works
Self-citationA free energy principle for a particular physics
Friston, K. (2019) · arXiv · doi:10.48550/arxiv.1906.10184 · Cited by 222 · see citing works
Self-citationThe power of predictions: An emerging paradigm for psychological research
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Planning and navigation as active inference
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Self-citationThe sense of should: A biologically-based framework for modeling social pressure
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Am i self-conscious? (or does self-organization entail self-consciousness?)
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Self-citationThe Anatomy of Inference: Generative Models and Brain Structure
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In the body's eye: the computational anatomy of interoceptive inference
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Self-citationActive Inference: Demystified and Compared
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Self-citationRegimes of Expectations: An Active Inference Model of Social Conformity and Human Decision Making
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Self-citationPredictive processing as a systematic basis for identifying the neural correlates of consciousness
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Self-citationThe free energy principle made simpler but not too simple
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“These beliefs are then used to evaluate the expected free energy of allowable policies, from which actions can be selected [123–125].”
InfluentialSelf-citationCOVID-19 detection from chest X-Ray images using Deep Learning and Convolutional Neural Networks
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Better Safe Than Sorry: A Common Signature of General Vulnerability for Psychopathology
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Self-citationComputational psychiatry: from synapses to sentience
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Self-citationDiverse motives for human curiosity
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“Hence the agent’s model must be able to entertain ‘counterfactually rich’ representations; i.e., beliefs about several alternative potential actions and the states of affairs that these actions would bring about (Friston et al., 2014, 2017c; Seth, 2014; Pezzulo, 2017; cf. Powers, 1973/2005).”
BackgroundMethodInfluentialSelf-citationPredictive Processing and the Representation Wars
Williams, D. (2017) · Minds and Machines · doi:10.1007/s11023-017-9441-6 · Cited by 146 · see citing works
Computational Neuropsychology and Bayesian Inference
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Self-citationMultiscale integration: beyond internalism and externalism
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Self-citationThe feeling of grip: novelty, error dynamics, and the predictive brain
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Neuronal oscillations: unavoidable and useful?
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An information-theoretic perspective on the costs of cognition
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Self-citationVariational ecology and the physics of sentient systems
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Self-citationA landscape of consciousness: Toward a taxonomy of explanations and implications
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“Beginning from this fundamental principle of nature (Hohwy, 2020), the FEP and Active Inference (FEP-AI) framework (Friston et al., 2017a) proscribes means of satisfying this imperative through minimizing prediction-error (or “free energy”) with respect to the models by which systems preserve…”
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Neuronal message passing using mean-field, bethe, and marginal approximations
Parr, T., Markovic, D., Kiebel, S. J., & Friston, K. J. (2019) · Scientific Reports · doi:10.1038/s41598-018-38246-3 · Cited by 128 · see citing works
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Self-citationThe evolution of brain architectures for predictive coding and active inference
Pezzulo, G., Parr, T., & Friston, K. J. (2021) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2020.0531 · Cited by 126 · see citing works
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Self-citationPlay in predictive minds: A cognitive theory of play.
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Path integrals, particular kinds, and strange things
Friston, K. J., Costa, L. D., Sakthivadivel, D. A. R., Heins, C., Pavliotis, G. A., Ramstead, M. J. D., & Parr, T. (2023) · Physics of Life Reviews · doi:10.1016/j.plrev.2023.08.016 · Cited by 122 · see citing works
Self-citationFields, C., & Levin, M. (2022) · Entropy · doi:10.3390/e24060819 · Cited by 121 · see citing works
A mathematical model of embodied consciousness.
Rudrauf, D., Bennequin, D., Granic, I., Landini, G., Friston, K., & Williford, K. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.05.032 · Cited by 118 · see citing works
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Self-citationOn markov blankets and hierarchical self-organisation
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Self-citationFrontal cortex function as derived from hierarchical predictive coding
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The math is not the territory: navigating the free energy principle
Andrews, M. (2021) · Biology & Philosophy · doi:10.1007/s10539-021-09807-0 · Cited by 115 · see citing works
Generative models, linguistic communication and active inference
Friston, K. J., Parr, T., Yufik, Y. M., Sajid, N., Price, C. J., & Holmes, E. (2020) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2020.07.005 · Cited by 113 · see citing works
Self-citationAn Active Inference Approach to Modeling Structure Learning: Concept Learning as an Example Case
Smith, R. S., Schwartenbeck, P., Parr, T., & Friston, K. J. (2020) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2020.00041 · Cited by 111 · see citing works
Self-citationActive inference as a theory of sentient behavior
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Self-citationInteroception as modeling, allostasis as control
Sennesh, E., Theriault, J., Brooks, D., van de Meent, J.-W., Barrett, L. F., & Quigley, K. S. (2022) · Biological Psychology · doi:10.1016/j.biopsycho.2021.108242 · Cited by 107 · see citing works
Predictive Coding: a Theoretical and Experimental Review
Millidge, B., Seth, A., & Buckley, C. L. (2021) · arXiv · doi:10.48550/arxiv.2107.12979 · Cited by 106 · see citing works
The first prior: From co-embodiment to co-homeostasis in early life
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Self-citationThe neurobiology of interoception and affect
Feldman, M. J., Bliss-Moreau, E., & Lindquist, K. A. (2024) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2024.01.009 · Cited by 101 · see citing works
A World Unto Itself: Human Communication as Active Inference
Vasil, J., Badcock, P. B., Constant, A., Friston, K. J., & Ramstead, M. J. D. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.00417 · Cited by 101 · see citing works
Self-citationDecision-making in schizophrenia: A predictive-coding perspective
Sterzer, P., Voss, M., Schlagenhauf, F., & Heinz, A. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2018.05.074 · Cited by 100 · see citing works
Ueltzhöffer, K. (2018) · Biological Cybernetics · doi:10.1007/s00422-018-0785-7 · Cited by 98 · see citing works
Free-energy minimization in joint agent-environment systems: A niche construction perspective
Bruineberg, J. P., Rietveld, E., Parr, T., van Maanen, L., & Friston, K. J. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.07.002 · Cited by 98 · see citing works
Self-citationThe active construction of the visual world
Parr, T., & Friston, K. J. (2017) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2017.08.003 · Cited by 97 · see citing works
Self-citationRepresentation Wars: Enacting an Armistice Through Active Inference
Constant, A., Clark, A., & Friston, K. J. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.598733 · Cited by 97 · see citing works
Self-citationWhence the Expected Free Energy?
Millidge, B., Tschantz, A., & Buckley, C. L. (2021) · Neural Computation · doi:10.1162/neco_a_01354 · Cited by 94 · see citing works
Internally generated hippocampal sequences as a vantage point to probe future‐oriented cognition
Pezzulo, G., Kemere, C. T., & van der Meer, M. A. A. (2017) · Annals of the New York Academy of Sciences · doi:10.1111/nyas.13329 · Cited by 93 · see citing works
Self-citationLinson, A., Clark, A., Ramamoorthy, S., & Friston, K. J. (2018) · Frontiers in Robotics and AI · doi:10.3389/frobt.2018.00021 · Cited by 93 · see citing works
Self-citationSmith, R., Lane, R. D., Parr, T., & Friston, K. J. (2019) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2019.09.002 · Cited by 89 · see citing works
Self-citationPerceptual awareness and active inference
Parr, T., Corcoran, A. W., Friston, K. J., & Hohwy, J. (2019) · Neuroscience of Consciousness · doi:10.1093/nc/niz012 · Cited by 91 · see citing works
Self-citationAction perception as hypothesis testing
Donnarumma, F., Costantini, M., Ambrosini, E., Friston, K., & Pezzulo, G. (2017) · Cortex · doi:10.1016/j.cortex.2017.01.016 · Cited by 90 · see citing works
Self-citationConcepts, goals and the control of survival-related behaviors
Feldman Barrett, L., & Finlay, B. L. (2018) · Current Opinion in Behavioral Sciences · doi:10.1016/j.cobeha.2018.10.001 · Cited by 89 · see citing works
World model learning and inference
Friston, K. J., Moran, R., Nagai, Y., Taniguchi, T., Gomi, H., & Tenenbaum, J. B. (2021) · Neural Networks · doi:10.1016/j.neunet.2021.09.011 · Cited by 89 · see citing works
Self-citationAllostasis as a core feature of hierarchical gradients in the human brain
Katsumi, Y., Theriault, J. E., Quigley, K. S., & Barrett, L. F. (2022) · Network Neuroscience · doi:10.1162/netn_a_00240 · Cited by 88 · see citing works
How particular is the physics of the free energy principle?
Aguilera, M., Millidge, B., Tschantz, A., & Buckley, C. L. (2021) · Physics of Life Reviews · doi:10.1016/j.plrev.2021.11.001 · Cited by 88 · see citing works
Precision and False Perceptual Inference
Parr, T., Benrimoh, D. A., Vincent, P., & Friston, K. J. (2018) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2018.00039 · Cited by 87 · see citing works
Self-citationLosing Ourselves: Active Inference, Depersonalization, and Meditation
Deane, G., Miller, M., & Wilkinson, S. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.539726 · Cited by 87 · see citing works
Conscious artificial intelligence and biological naturalism
Seth, A. K. (2026) · Behavioral and Brain Sciences · doi:10.1017/s0140525x25000032 · Cited by 87 · see citing works
Leptourgos, P., Fortier, M., Carhart-Harris, R. L., Corlett, P. R., Dupuis, D., Halberstadt, A. L., Kometer, M., Kozáková, E., Larøi, F., Noorani, T. N., et al. (2020) · Schizophrenia Bulletin · doi:10.1093/schbul/sbaa117 · Cited by 87 · see citing works
A free energy principle for generic quantum systems
Fields, C., Friston, K. J., Glazebrook, J. F., & Levin, M. (2022) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2022.05.006 · Cited by 87 · see citing works
Self-citationCiaunica, A., Seth, A. K., Limanowski, J., Hesp, C., & Friston, K. J. (2022) · Consciousness and Cognition · doi:10.1016/j.concog.2022.103320 · Cited by 86 · see citing works
Self-citation
- Authors
- Friston, K., FitzGerald, T., Rigoli, F., Schwartenbeck, P., & Pezzulo, G.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- National Research Council (IT)
- Corresponding author
- Friston, Karl
- FitzGerald, Thomas
- Rigoli, Francesco
- Schwartenbeck, Philipp
- Pezzulo, Giovanni
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 2017-01
- Volume
- 29
- Issue
- 1
- Pages
- 1-49
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2552810632
- Cited by
- 1,156
- References
- 113
- Citations by year
- 2026: 142 · 2025: 145 · 2024: 124 · 2023: 129 · 2022: 145 · 2021: 147 · 2020: 155 · 2019: 73 · 2018: 61 · 2017: 35
- FWCI
- 35.50
- Type
- journal article
- Language
- en
- Open access
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- City Research Online (City University London) (submittedVersion)
- UEA Digital Repository (University of East Anglia) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- Wellcome Trust (088130/Z/09/Z)
- Österreichischen Akademie der Wissenschaften
- Universität Salzburg
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Embodied and Extended Cognition
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Keywords
- active inference, variational free energy, marginal likelihood, gradient descent, neural dynamics, Markov decision process, repetition suppression, mismatch negativity, place cells, phase precession, theta sequences, theta-gamma coupling, evidence accumulation, dopamine, reward seeking, contextual learning, Lyapunov function, Hamilton's principle of least action, action selection
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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