{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T18:51:32Z","timestamp":1778611892152,"version":"3.51.4"},"reference-count":124,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2020,12,3]],"date-time":"2020-12-03T00:00:00Z","timestamp":1606953600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information processing of perception.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008420","type":"journal-article","created":{"date-parts":[[2020,12,3]],"date-time":"2020-12-03T18:29:26Z","timestamp":1607020166000},"page":"e1008420","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":33,"title":["The two kinds of free energy and the Bayesian revolution"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2906-3577","authenticated-orcid":true,"given":"Sebastian","family":"Gottwald","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel A.","family":"Braun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2020,12,3]]},"reference":[{"issue":"7","key":"pcbi.1008420.ref001","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.tics.2006.05.002","article-title":"Vision as Bayesian inference: analysis by synthesis?","volume":"10","author":"A Yuille","year":"2006","journal-title":"Trends in Cognitive Sciences"},{"issue":"6","key":"pcbi.1008420.ref002","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/S0959-4388(99)00028-8","article-title":"Internal models for motor control and trajectory planning","volume":"9","author":"M Kawato","year":"1999","journal-title":"Current Opinion in Neurobiology"},{"issue":"2","key":"pcbi.1008420.ref003","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/S0960-9822(03)00007-1","article-title":"Prediction Precedes Control in Motor Learning","volume":"13","author":"JR Flanagan","year":"2003","journal-title":"Current Biology"},{"key":"pcbi.1008420.ref004","volume-title":"Bayesian Brain: Probabilistic Approaches to Neural Coding","author":"K Doya","year":"2007"},{"issue":"5","key":"pcbi.1008420.ref005","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1162\/neco.1995.7.5.889","article-title":"The Helmholtz Machine","volume":"7","author":"P Dayan","year":"1995","journal-title":"Neural Comput"},{"key":"pcbi.1008420.ref006","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/978-94-011-5014-9_12","volume-title":"Learning in Graphical Models","author":"RM Neal","year":"1998"},{"key":"pcbi.1008420.ref007","volume-title":"Variational Algorithms for Approximate Bayesian Inference","author":"MJ Beal","year":"2003"},{"issue":"3","key":"pcbi.1008420.ref008","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/09540099108946587","article-title":"Function Optimization using Connectionist Reinforcement Learning Algorithms","volume":"3","author":"RJ Williams","year":"1991","journal-title":"Connection Science"},{"key":"pcbi.1008420.ref009","unstructured":"Mnih V, Badia AP, Mirza M, Graves A, Lillicrap T, Harley T, et al. Asynchronous Methods for Deep Reinforcement Learning. In: Balcan MF, Weinberger KQ, editors. Proceedings of The 33rd International Conference on Machine Learning. vol. 48 of Proceedings of Machine Learning Research. New York, New York, USA: PMLR; 2016. p. 1928\u20131937. http:\/\/proceedings.mlr.press\/v48\/mniha16.html."},{"issue":"1","key":"pcbi.1008420.ref010","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1006\/game.1995.1023","article-title":"Quantal Response Equilibria for Normal Form Games","volume":"10","author":"RD McKelvey","year":"1995","journal-title":"Games and Economic Behavior"},{"issue":"3","key":"pcbi.1008420.ref011","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/S0304-3932(03)00029-1","article-title":"Implications of rational inattention","volume":"50","author":"CA Sims","year":"2003","journal-title":"Journal of Monetary Economics"},{"issue":"1","key":"pcbi.1008420.ref012","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/S0899-8256(02)00014-3","article-title":"Probabilistic choice and procedurally bounded rationality","volume":"41","author":"LG Mattsson","year":"2002","journal-title":"Games and Economic Behavior"},{"issue":"2","key":"pcbi.1008420.ref013","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s00199-004-0495-3","article-title":"Revealed stochastic preference: a synthesis","volume":"26","author":"DL McFadden","year":"2005","journal-title":"Economic Theory"},{"key":"pcbi.1008420.ref014","first-page":"262","volume-title":"Information Theory\u2014The Bridge Connecting Bounded Rational Game Theory and Statistical Physics","author":"DH Wolpert","year":"2006"},{"issue":"6","key":"pcbi.1008420.ref015","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1111\/j.1468-0262.2006.00716.x","article-title":"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences","volume":"74","author":"F Maccheroni","year":"2006","journal-title":"Econometrica"},{"key":"pcbi.1008420.ref016","doi-asserted-by":"crossref","DOI":"10.1515\/9781400829385","volume-title":"Robustness","author":"LP Hansen","year":"2008"},{"issue":"2","key":"pcbi.1008420.ref017","doi-asserted-by":"crossref","first-page":"28005","DOI":"10.1209\/0295-5075\/85\/28005","article-title":"Information-theoretic approach to interactive learning","volume":"85","author":"S Still","year":"2009","journal-title":"Europhysics Letters"},{"key":"pcbi.1008420.ref018","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1007\/978-1-4419-1452-1_19","volume-title":"Perception-Action Cycle: Models, Architectures, and Hardware","author":"N Tishby","year":"2011"},{"issue":"2153","key":"pcbi.1008420.ref019","doi-asserted-by":"crossref","first-page":"20120683","DOI":"10.1098\/rspa.2012.0683","article-title":"Thermodynamics as a theory of decision-making with information-processing costs","volume":"469","author":"PA Ortega","year":"2013","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1008420.ref020","unstructured":"Ortega PA, Stocker A. Human Decision-Making under Limited Time. In: 30th Conference on Neural Information Processing Systems; 2016."},{"key":"pcbi.1008420.ref021","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.cognition.2016.03.020","article-title":"Rate\u2013distortion theory and human perception","volume":"152","author":"CR Sims","year":"2016","journal-title":"Cognition"},{"key":"pcbi.1008420.ref022","doi-asserted-by":"crossref","first-page":"932","DOI":"10.3389\/fnins.2018.00932","article-title":"Quantifying Motor Task Performance by Bounded Rational Decision Theory","volume":"12","author":"S Schach","year":"2018","journal-title":"Frontiers in Neuroscience"},{"key":"pcbi.1008420.ref023","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.3389\/fnins.2019.01230","article-title":"Analyzing Abstraction and Hierarchical Decision-Making in Absolute Identification by Information-Theoretic Bounded Rationality","volume":"13","author":"C Lindig-Le\u00f3n","year":"2019","journal-title":"Frontiers in Neuroscience"},{"issue":"6","key":"pcbi.1008420.ref024","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1037\/rev0000123","article-title":"Decision by sampling implements efficient coding of psychoeconomic functions","volume":"125","author":"R Bhui","year":"2018","journal-title":"Psychological Review"},{"key":"pcbi.1008420.ref025","doi-asserted-by":"crossref","unstructured":"Ho MK, Abel D, Cohen JD, Littman ML, Griffiths TL. The Efficiency of Human Cognition Reflects Planned Information Processing. 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Predictive brains, situated agents, and the future of cognitive science","volume":"36","author":"A Clark","year":"2013","journal-title":"Behavioral and Brain Sciences"},{"key":"pcbi.1008420.ref039","article-title":"First principles in the life sciences: the free-energy principle, organicism, and mechanism","author":"M Colombo","year":"2018","journal-title":"Synthese"},{"key":"pcbi.1008420.ref040","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/B978-0-08-051489-5.50010-2","volume-title":"Probabilistic Reasoning in Intelligent Systems","author":"J Pearl","year":"1988"},{"key":"pcbi.1008420.ref041","unstructured":"Minka TP. Expectation Propagation for Approximate Bayesian Inference. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence. UAI\u201901. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.; 2001. p. 362\u2013369."},{"key":"pcbi.1008420.ref042","doi-asserted-by":"crossref","unstructured":"Hinton GE, van Camp D. Keeping the Neural Networks Simple by Minimizing the Description Length of the Weights. In: Proceedings of the Sixth Annual Conference on Computational Learning Theory. COLT\u201993. New York, NY, USA: ACM; 1993. p. 5\u201313.","DOI":"10.1145\/168304.168306"},{"key":"pcbi.1008420.ref043","volume-title":"Information Theory, Inference & Learning Algorithms","author":"DJC MacKay","year":"2002"},{"issue":"1","key":"pcbi.1008420.ref044","first-page":"1","article-title":"Decision-Theoretic Planning: Structural Assumptions and Computational Leverage","volume":"11","author":"C Boutilier","year":"1999","journal-title":"J Artif Int Res"},{"key":"pcbi.1008420.ref045","volume-title":"Advanced book program","author":"RP Feynman","year":"1996"},{"key":"pcbi.1008420.ref046","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"ET Jaynes","year":"1957","journal-title":"Phys Rev"},{"key":"pcbi.1008420.ref047","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511790423","volume-title":"Probability Theory","author":"ET Jaynes","year":"2003"},{"key":"pcbi.1008420.ref048","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-6581-2","volume-title":"E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics","author":"RD Rosenkrantz","year":"1983"},{"key":"pcbi.1008420.ref049","volume-title":"Ars conjectandi","author":"J Bernoulli","year":"1713"},{"key":"pcbi.1008420.ref050","volume-title":"Th\u00e9orie analytique des probabilit\u00e9s","author":"PS de Laplace","year":"1812"},{"key":"pcbi.1008420.ref051","volume-title":"Calcul des probabilit\u00e9s","author":"H Poincar\u00e9","year":"1912"},{"issue":"2","key":"pcbi.1008420.ref052","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/bjps\/31.2.131","article-title":"Bayesian Conditionalisation and the Principle of Minimum Information","volume":"31","author":"PM Williams","year":"1980","journal-title":"The British Journal for the Philosophy of Science"},{"key":"pcbi.1008420.ref053","unstructured":"Haarnoja T, Tang H, Abbeel P, Levine S. Reinforcement Learning with Deep Energy-Based Policies. In: ICML; 2017."},{"key":"pcbi.1008420.ref054","unstructured":"Fox R, Pakman A, Tishby N. Taming the Noise in Reinforcement Learning via Soft Updates. In: Proceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence. UAI\u201916. Arlington, Virginia, United States: AUAI Press; 2016. p. 202\u2013211. http:\/\/dl.acm.org\/citation.cfm?id=3020948.3020970."},{"key":"pcbi.1008420.ref055","volume-title":"Probabilistic graphical models: principles and techniques","author":"D Koller","year":"2009"},{"key":"pcbi.1008420.ref056","doi-asserted-by":"crossref","unstructured":"Opper M, Saad D. In: Comparing the Mean Field Method and Belief Propagation for Approximate Inference in MRFs; 2001. p. 229\u2013239.","DOI":"10.7551\/mitpress\/1100.003.0019"},{"issue":"1","key":"pcbi.1008420.ref057","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum Likelihood from Incomplete Data via the EM Algorithm","volume":"39","author":"AP Dempster","year":"1977","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"key":"pcbi.1008420.ref058","first-page":"689","volume-title":"Advances in Neural Information Processing Systems 13","author":"JS Yedidia","year":"2001"},{"issue":"11","key":"pcbi.1008420.ref059","doi-asserted-by":"crossref","first-page":"3697","DOI":"10.1109\/TIT.2005.856938","article-title":"MAP estimation via agreement on (hyper)trees: Message-passing and linear-programming approaches","volume":"51","author":"MJ Wainwright","year":"2005","journal-title":"IEEE Transactions on Information Theory"},{"key":"pcbi.1008420.ref060","first-page":"661","article-title":"Variational Message Passing","volume":"6","author":"J Winn","year":"2005","journal-title":"J Mach Learn Res"},{"key":"pcbi.1008420.ref061","unstructured":"Minka T. Divergence Measures and Message Passing. Microsoft; 2005. MSR-TR-2005-173."},{"issue":"7","key":"pcbi.1008420.ref062","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1109\/TIT.2005.850085","article-title":"Constructing free-energy approximations and generalized belief propagation algorithms","volume":"51","author":"JS Yedidia","year":"2005","journal-title":"IEEE Transactions on Information Theory"},{"key":"pcbi.1008420.ref063","first-page":"205","article-title":"Information geometry and alternating minimization procedures","volume":"1","author":"I Csisz\u00e1r","year":"1984","journal-title":"Statistics and Decisions, Supplement Issue"},{"issue":"2","key":"pcbi.1008420.ref064","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0167-7152(86)90016-7","article-title":"Another interpretation of the EM algorithm for mixture distributions","volume":"4","author":"RJ Hathaway","year":"1986","journal-title":"Statistics & Probability Letters"},{"key":"pcbi.1008420.ref065","first-page":"359","volume-title":"Advances in Neural Information Processing Systems 15","author":"T Heskes","year":"2003"},{"issue":"7","key":"pcbi.1008420.ref066","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1162\/08997660260028674","article-title":"CCCP Algorithms to Minimize the Bethe and Kikuchi Free Energies: Convergent Alternatives to Belief Propagation","volume":"14","author":"AL Yuille","year":"2002","journal-title":"Neural Computation"},{"key":"pcbi.1008420.ref067","first-page":"416","volume-title":"Nobel prizes, presentations, biographies, & lectures","author":"D Kahneman","year":"2002"},{"key":"pcbi.1008420.ref068","volume-title":"Theory of Games and Economic Behavior","author":"J von Neumann","year":"1944"},{"key":"pcbi.1008420.ref069","volume-title":"Risk-sensitive optimal control","author":"P Whittle","year":"1990"},{"key":"pcbi.1008420.ref070","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/978-3-319-46227-1_30","volume-title":"Machine Learning and Knowledge Discovery in Databases","author":"J Grau-Moya","year":"2016"},{"issue":"2","key":"pcbi.1008420.ref071","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1162\/neco_a_01153","article-title":"Systems of bounded rational agents with information-theoretic constraints","volume":"31","author":"S Gottwald","year":"2019","journal-title":"Neural Computation"},{"issue":"1","key":"pcbi.1008420.ref072","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2307\/1884852","article-title":"A Behavioral Model of Rational Choice","volume":"69","author":"HA Simon","year":"1955","journal-title":"The Quarterly Journal of Economics"},{"key":"pcbi.1008420.ref073","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68276-1","volume-title":"Inequalities: Theory of Majorization and Its Applications","author":"AW Marshall","year":"2011","edition":"2"},{"issue":"4","key":"pcbi.1008420.ref074","doi-asserted-by":"crossref","DOI":"10.3390\/e21040375","article-title":"Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty","volume":"21","author":"S Gottwald","year":"2019","journal-title":"Entropy"},{"issue":"4","key":"pcbi.1008420.ref075","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.3982\/ECTA7801","article-title":"A Unique Costly Contemplation Representation","volume":"78","author":"H Ergin","year":"2010","journal-title":"Econometrica"},{"issue":"28","key":"pcbi.1008420.ref076","doi-asserted-by":"crossref","first-page":"11478","DOI":"10.1073\/pnas.0710743106","article-title":"Efficient computation of optimal actions","volume":"106","author":"E Todorov","year":"2009","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"pcbi.1008420.ref077","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10994-012-5278-7","article-title":"Optimal control as a graphical model inference problem","volume":"87","author":"HJ Kappen","year":"2012","journal-title":"Machine Learning"},{"key":"pcbi.1008420.ref078","doi-asserted-by":"crossref","unstructured":"Binz M, Gershman SJ, Schulz E, Endres D. Heuristics From Bounded Meta-Learned Inference. 2020;","DOI":"10.31234\/osf.io\/5du2b"},{"issue":"19","key":"pcbi.1008420.ref079","doi-asserted-by":"crossref","first-page":"193001","DOI":"10.1088\/1751-8121\/ab0850","article-title":"The stochastic thermodynamics of computation","volume":"52","author":"DH Wolpert","year":"2019","journal-title":"Journal of Physics A: Mathematical and Theoretical"},{"issue":"2","key":"pcbi.1008420.ref080","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1037\/h0043158","article-title":"The magical number seven, plus or minus two: some limits on our capacity for processing information","volume":"63","author":"GA Miller","year":"1956","journal-title":"Psychological Review"},{"key":"pcbi.1008420.ref081","volume-title":"Uncertainty and structure as psychological concepts","author":"WR Garner","year":"1962"},{"issue":"2","key":"pcbi.1008420.ref082","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1037\/h0028513","article-title":"Channel capacity in absolute judgment tasks: An artifact of information bias?","volume":"73","author":"AW MacRae","year":"1970","journal-title":"Psychological Bulletin"},{"issue":"7","key":"pcbi.1008420.ref083","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/TAC.2004.831187","article-title":"Control Under Communication Constraints","volume":"49","author":"S Tatikonda","year":"2004","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"pcbi.1008420.ref084","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/TIT.2009.2034824","article-title":"The Communication Complexity of Correlation","volume":"56","author":"P Harsha","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"key":"pcbi.1008420.ref085","doi-asserted-by":"crossref","DOI":"10.3389\/frobt.2015.00027","article-title":"Bounded Rationality, Abstraction, and Hierarchical Decision-Making: An Information-Theoretic Optimality Principle","volume":"2","author":"T Genewein","year":"2015","journal-title":"Frontiers in Robotics and AI"},{"issue":"3","key":"pcbi.1008420.ref086","doi-asserted-by":"crossref","first-page":"261","DOI":"10.3390\/e10030261","article-title":"Axiomatic Characterizations of Information Measures","volume":"10","author":"I Csisz\u00e1r","year":"2008","journal-title":"Entropy"},{"issue":"1","key":"pcbi.1008420.ref087","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1613\/jair.133","article-title":"Provably Bounded-optimal Agents","volume":"2","author":"SJ Russell","year":"1995","journal-title":"Journal of Artificial Intelligence Research"},{"key":"pcbi.1008420.ref088","volume-title":"Bounded Rationality: The Adaptive Toolbox","author":"G Gigerenzer","year":"2001"},{"issue":"1","key":"pcbi.1008420.ref089","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1186\/2194-3206-2-2","article-title":"Generalized Thompson sampling for sequential decision-making and causal inference","volume":"2","author":"PA Ortega","year":"2014","journal-title":"Complex Adaptive Systems Modeling"},{"key":"pcbi.1008420.ref090","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"CE Shannon","year":"1948","journal-title":"The Bell System Technical Journal"},{"key":"pcbi.1008420.ref091","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jphysparis.2006.10.001","article-title":"A free energy principle for the brain","volume":"100","author":"KJ Friston","year":"2006","journal-title":"Journal of Physiology-Paris"},{"key":"pcbi.1008420.ref092","doi-asserted-by":"crossref","unstructured":"Gershman SJ. What does the free energy principle tell us about the brain. Neurons, Behavior, Data Analysis, and Theory. 2019;","DOI":"10.51628\/001c.10839"},{"key":"pcbi.1008420.ref093","volume-title":"Cybernetics: Or Control and Communication in the Animal and the Machine","author":"N Wiener","year":"1948"},{"key":"pcbi.1008420.ref094","doi-asserted-by":"crossref","DOI":"10.1037\/11592-000","volume-title":"Design for a Brain: The Origin of Adaptive Behavior","author":"W Ashby","year":"1960"},{"key":"pcbi.1008420.ref095","volume-title":"Behavior: The Control of Perception","author":"WT Powers","year":"1973"},{"issue":"11-12","key":"pcbi.1008420.ref096","first-page":"125","article-title":"Beyond the computer metaphor: behaviour as interaction","volume":"6","author":"P Cisek","year":"1999","journal-title":"Journal of Consciousness Studies"},{"issue":"86","key":"pcbi.1008420.ref097","doi-asserted-by":"crossref","first-page":"20130475","DOI":"10.1098\/rsif.2013.0475","article-title":"Life as we know it","volume":"10","author":"K Friston","year":"2013","journal-title":"Journal of The Royal Society Interface"},{"key":"pcbi.1008420.ref098","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198811930.003.0015","volume-title":"Allostasis, interoception, and the free energy principle: Feeling our way forward","author":"AW Corcoran","year":"2018"},{"key":"pcbi.1008420.ref099","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1016\/j.neubiorev.2016.06.022","article-title":"Active inference and learning","volume":"68","author":"K Friston","year":"2016","journal-title":"Neuroscience & Biobehavioral Reviews"},{"key":"pcbi.1008420.ref100","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/NECO_a_00912","article-title":"Active Inference: A Process Theory","volume":"29","author":"KJ Friston","year":"2017","journal-title":"Neural Computation"},{"issue":"9","key":"pcbi.1008420.ref101","doi-asserted-by":"crossref","first-page":"2530","DOI":"10.1162\/neco_a_01108","article-title":"Active Inference, Belief Propagation, and the Bethe Approximation","volume":"30","author":"S Schw\u00f6bel","year":"2018","journal-title":"Neural Computation"},{"issue":"1","key":"pcbi.1008420.ref102","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1038\/s41598-018-38246-3","article-title":"Neuronal message passing using Mean-field, Bethe, and Marginal approximations","volume":"9","author":"T Parr","year":"2019","journal-title":"Scientific Reports"},{"issue":"6","key":"pcbi.1008420.ref103","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1103\/PhysRev.81.988","article-title":"A Theory of Cooperative Phenomena","volume":"81","author":"R Kikuchi","year":"1951","journal-title":"Physical Review"},{"key":"pcbi.1008420.ref104","volume-title":"The Logic of Decision","author":"RC Jeffrey","year":"1965","edition":"1"},{"key":"pcbi.1008420.ref105","doi-asserted-by":"crossref","unstructured":"Toussaint M, Storkey A. Probabilistic Inference for Solving Discrete and Continuous State Markov Decision Processes. In: Proceedings of the 23rd International Conference on Machine Learning. ICML\u201906. New York, NY, USA: Association for Computing Machinery; 2006. p. 945\u2013952.","DOI":"10.1145\/1143844.1143963"},{"key":"pcbi.1008420.ref106","doi-asserted-by":"crossref","unstructured":"Todorov E. General duality between optimal control and estimation. In: 2008 47th IEEE Conference on Decision and Control. IEEE; 2008.","DOI":"10.1109\/CDC.2008.4739438"},{"key":"pcbi.1008420.ref107","unstructured":"Levine S. Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. arXiv:180500909. 2018;."},{"key":"pcbi.1008420.ref108","unstructured":"O\u2019Donoghue B, Osband I, Ionescu C. Making Sense of Reinforcement Learning and Probabilistic Inference. In: International Conference on Learning Representations. ICLR\u201920; 2020."},{"key":"pcbi.1008420.ref109","doi-asserted-by":"crossref","unstructured":"Toussaint M. Robot trajectory optimization using approximate inference. In: Proceedings of the 26th Annual International Conference on Machine Learning\u2014ICML\u201909. ACM Press; 2009. https:\/\/doi.org\/10.1145%2F1553374.1553508","DOI":"10.1145\/1553374.1553508"},{"key":"pcbi.1008420.ref110","volume-title":"Modeling Purposeful Adaptive Behavior with the Principle of Maximum Causal Entropy","author":"BD Ziebart","year":"2010"},{"issue":"4","key":"pcbi.1008420.ref111","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1017\/S0140525X01000061","article-title":"Generalization, similarity, and Bayesian inference","volume":"24","author":"JB Tenenbaum","year":"2001","journal-title":"Behavioral and Brain Sciences"},{"key":"pcbi.1008420.ref112","volume-title":"Principles of Brain Dynamics","author":"SJ Gershman","year":"2012"},{"issue":"2","key":"pcbi.1008420.ref113","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1162\/neco.1997.9.2.271","article-title":"Using Expectation-Maximization for Reinforcement Learning","volume":"9","author":"P Dayan","year":"1997","journal-title":"Neural Computation"},{"key":"pcbi.1008420.ref114","doi-asserted-by":"crossref","unstructured":"Biehl M, Pollock FA, Kanai R. A technical critique of the free energy principle as presented in \u201cLife as we know it\u201d and related works. arXiv:200106408. 2020;.","DOI":"10.3390\/e23030293"},{"key":"pcbi.1008420.ref115","doi-asserted-by":"crossref","unstructured":"Friston K, Costa LD, Parr T. Some interesting observations on the free energy principle. arXiv:200204501. 2020;.","DOI":"10.3390\/e23081076"},{"key":"pcbi.1008420.ref116","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4643.001.0001","volume-title":"The Minimum Description Length Principle","author":"P Gr\u00fcnwald","year":"2007"},{"issue":"10","key":"pcbi.1008420.ref117","first-page":"3434","article-title":"The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes","volume":"25","author":"P Schwartenbeck","year":"2015","journal-title":"Cerebral cortex (New York, NY: 1991)"},{"issue":"4","key":"pcbi.1008420.ref118","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1162\/NETN_a_00018","article-title":"The graphical brain: Belief propagation and active inference","volume":"1","author":"KJ Friston","year":"2017","journal-title":"Network Neuroscience"},{"key":"pcbi.1008420.ref119","doi-asserted-by":"crossref","first-page":"39","DOI":"10.3389\/fnint.2018.00039","article-title":"Precision and False Perceptual Inference","volume":"12","author":"T Parr","year":"2018","journal-title":"Frontiers in Integrative Neuroscience"},{"issue":"1","key":"pcbi.1008420.ref120","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1038\/4580","article-title":"Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects","volume":"2","author":"RPN Rao","year":"1999","journal-title":"Nature Neuroscience"},{"key":"pcbi.1008420.ref121","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.conb.2017.08.010","article-title":"With or without you: predictive coding and Bayesian inference in the brain","volume":"46","author":"L Aitchison","year":"2017","journal-title":"Current Opinion in Neurobiology"},{"key":"pcbi.1008420.ref122","article-title":"Self-supervision, normativity and the free energy principle","author":"J Hohwy","year":"2020","journal-title":"Synthese"},{"key":"pcbi.1008420.ref123","volume-title":"Animal behavior: an evolutionary approach","author":"J Alcock","year":"1993"},{"key":"pcbi.1008420.ref124","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1111\/j.1439-0310.1963.tb01161.x","article-title":"On aims and methods of Ethology","volume":"20","author":"N Tinbergen","year":"1963","journal-title":"Zeitschrift f\u00fcr Tierpsychologie"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,18]],"date-time":"2024-08-18T13:50:17Z","timestamp":1723989017000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008420"}},"subtitle":[],"editor":[{"given":"Samuel J.","family":"Gershman","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2020,12,3]]},"references-count":124,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12,3]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008420","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,3]]}}}