{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T08:39:18Z","timestamp":1780735158549,"version":"3.54.1"},"reference-count":91,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T00:00:00Z","timestamp":1589414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010269","name":"Wellcome Trust","doi-asserted-by":"publisher","award":["088130\/Z\/09\/Z"],"award-info":[{"award-number":["088130\/Z\/09\/Z"]}],"id":[{"id":"10.13039\/100010269","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MR\/S502522\/1"],"award-info":[{"award-number":["MR\/S502522\/1"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised \u2018modules\u2019, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.<\/jats:p>","DOI":"10.3390\/e22050552","type":"journal-article","created":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T10:53:59Z","timestamp":1589540039000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Modules or Mean-Fields?"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5108-5743","authenticated-orcid":false,"given":"Thomas","family":"Parr","sequence":"first","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging (UCL), London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noor","family":"Sajid","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging (UCL), London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":false,"given":"Karl J.","family":"Friston","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging (UCL), London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fodor, J.A. (1983). The Modularity of Mind: An Essay on Faculty Psychology, reprint ed., MIT Press.","DOI":"10.7551\/mitpress\/4737.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/02643294.2011.558835","article-title":"Modules and brain mapping","volume":"28","author":"Friston","year":"2011","journal-title":"Cogn. Neuropsychol."},{"key":"ref_3","first-page":"20122863","article-title":"The evolutionary origins of modularity","volume":"280","author":"Clune","year":"2013","journal-title":"Biol. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hipolito, I., and Kirchhoff, M.D. (2020, May 13). The Predictive Brain: A Modular View of Brain and Cognitive Function? preprints, 2019. Available online: https:\/\/www.preprints.org\/manuscript\/201911.0111\/v1.","DOI":"10.20944\/preprints201911.0111.v1"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Baltieri, M., and Buckley, C.L. (2018). The modularity of action and perception revisited using control theory and active inference. Artificial Life Conference Proceedings, MIT Press.","DOI":"10.1162\/isal_a_00031"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cosmides, L., and Tooby, J. (1994). Origins of domain specificity: The evolution of functional organization. Mapping the Mind: Domain Specificity in Cognition and Culture, Cambridge University Press.","DOI":"10.1017\/CBO9780511752902.005"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1051\/jphystap:019070060066100","article-title":"L\u2019hypoth\u00e8se du champ mol\u00e9culaire et la propri\u00e9t\u00e9 ferromagn\u00e9tique","volume":"6","author":"Weiss","year":"1907","journal-title":"J. Phys. Theor. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/s10955-009-9814-1","article-title":"More is the Same; Phase Transitions and Mean Field Theories","volume":"137","author":"Kadanoff","year":"2009","journal-title":"J. Stat. Phys."},{"key":"ref_9","unstructured":"Cessac, B. (2020, May 13). Mean Field Methods in Neuroscience. Available online: https:\/\/core.ac.uk\/download\/pdf\/52775181.pdf."},{"key":"ref_10","unstructured":"Fasoli, D. (2013). Attacking the Brain with Neuroscience: Mean-Field Theory, Finite Size Effects and Encoding Capability of Stochastic Neural Networks. [Ph.D. Thesis, Universit\u00e9 Nice Sophia Antipolis]."},{"key":"ref_11","first-page":"661","article-title":"Variational message passing","volume":"6","author":"Winn","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Gadomski, A., Kruszewska, N., Ausloos, M., and Tadych, J. (2007). On the Harmonic-Mean Property of Model Dispersive Systems Emerging Under Mononuclear, Mixed and Polynuclear Path Conditions. Traffic and Granular Flow\u201905, Springer.","DOI":"10.1007\/978-3-540-47641-2_24"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Levin, S.A., Hallam, T.G., and Gross, L.J. (1989). Three Basic Epidemiological Models. Applied Mathematical Ecology, Springer.","DOI":"10.1007\/978-3-642-61317-3"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11537-007-0657-8","article-title":"Mean field games","volume":"2","author":"Lasry","year":"2007","journal-title":"Jpn. J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lelarge, M., and Bolot, J. (2008, January 20\u201322). A local mean field analysis of security investments in networks. Proceedings of the 3rd international workshop on Economics of networked systems, Seattle, WA, USA.","DOI":"10.1145\/1403027.1403034"},{"key":"ref_16","unstructured":"Friston, K. (2019). A free energy principle for a particular physics. arXiv."},{"key":"ref_17","unstructured":"Yoshioka, D. (2007). The Partition Function and the Free Energy. Statistical Physics: An Introduction, Springer."},{"key":"ref_18","unstructured":"Hinton, G.E., and Zemel, R.S. (1994). Autoencoders, minimum description length and Helmholtz free energy. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_19","unstructured":"Beal, M.J. (2003). Variational Algorithms for Approximate Bayesian Inference, University of London."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1016\/0031-8914(66)90024-3","article-title":"On model dynamical systems in statistical mechanics","volume":"32","author":"Bogolyubov","year":"1966","journal-title":"Physica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1103\/RevModPhys.20.367","article-title":"Space-Time Approach to Non-Relativistic Quantum Mechanics","volume":"20","author":"Feynman","year":"1948","journal-title":"Rev. Mod. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MSP.2004.1267047","article-title":"An introduction to factor graphs","volume":"21","author":"Loeliger","year":"2004","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Vontobel, P.O. (2011). A factor-graph approach to Lagrangian and Hamiltonian dynamics. 2011 IEEE International Symposium on Information Theory Proceedings, IEEE.","DOI":"10.1109\/ISIT.2011.6033945"},{"key":"ref_24","first-page":"5642","article-title":"Factor Graphs for Quantum Probabilities","volume":"63","author":"Loeliger","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"90","DOI":"10.3389\/fncom.2018.00090","article-title":"The Anatomy of Inference: Generative Models and Brain Structure","volume":"12","author":"Parr","year":"2018","journal-title":"Front. Comput. Neurosci."},{"key":"ref_26","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":"Friston","year":"2017","journal-title":"Netw. Neurosci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"R309","DOI":"10.1088\/0305-4470\/38\/33\/R01","article-title":"Cluster variation method in statistical physics and probabilistic graphical models","volume":"38","author":"Pelizzola","year":"2005","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_28","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":"Yedidia","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","unstructured":"Frey, B.J., and MacKay, D.J.C. A revolution: Belief propagation in graphs with cycles. Proceedings of the 1997 Conference on Advances in Neural Information Processing Systems 10."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Risken, H. (1996). Fokker-Planck Equation. The Fokker-Planck Equation: Methods of Solution and Applications, Springer.","DOI":"10.1007\/978-3-642-61544-3"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"L25","DOI":"10.1088\/0305-4470\/37\/3\/L01","article-title":"Potential in stochastic differential equations: Novel construction","volume":"3","author":"Ao","year":"2004","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"13029","DOI":"10.1073\/pnas.0506347102","article-title":"Structure of stochastic dynamics near fixed points","volume":"102","author":"Kwon","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_33","unstructured":"Ma, Y.-A., Chen, T., and Fox, E. (2015). A complete recipe for stochastic gradient MCMC. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1017\/S0140525X99002022","article-title":"Is vision continuous with cognition? The case for cognitive impenetrability of visual perception","volume":"22","author":"Pylyshyn","year":"1999","journal-title":"Behav. Brain Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"126001","DOI":"10.1088\/0034-4885\/75\/12\/126001","article-title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","volume":"75","author":"Seifert","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3591","DOI":"10.1021\/nn100869j","article-title":"Directed Self-Assembly of Nanoparticles","volume":"4","author":"Grzelczak","year":"2010","journal-title":"ACS Nano"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1038\/nmat1211","article-title":"Nanostructure engineering by templated self-assembly of block copolymers","volume":"3","author":"Cheng","year":"2004","journal-title":"Nat. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.neuroimage.2008.10.008","article-title":"Population dynamics under the Laplace assumption","volume":"44","author":"Marreiros","year":"2009","journal-title":"Neuroimage"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3389\/fncom.2013.00057","article-title":"Neural masses and fields in dynamic causal modeling","volume":"7","author":"Moran","year":"2013","journal-title":"Front. Comput. Neurosci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"Monte Carlo sampling methods using Markov chains and their applications","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika"},{"key":"ref_41","unstructured":"Yildirim, I. (2012). Bayesian inference: Gibbs sampling, University of Rochester. Technical Note."},{"key":"ref_42","unstructured":"Neal, R.M. (1993). Probabilistic Inference Using Markov Chain Monte Carlo Methods, Department of Computer Science, University of Toronto."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/j.1467-9868.2010.00765.x","article-title":"Riemann manifold Langevin and Hamiltonian Monte Carlo methods","volume":"73","author":"Girolami","year":"2011","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0959-4388(94)90066-3","article-title":"\u2018What\u2019 and \u2018where\u2019 in the human brain","volume":"4","author":"Ungerleider","year":"1994","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1098\/rstb.2011.0359","article-title":"Multistability in auditory stream segregation: A predictive coding view","volume":"367","author":"Winkler","year":"2012","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.cognition.2003.10.011","article-title":"Dorsal and ventral streams: A framework for understanding aspects of the functional anatomy of language","volume":"92","author":"Hickok","year":"2004","journal-title":"Cognition"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.tics.2016.05.001","article-title":"The Functional Anatomy of Time: What and When in the Brain","volume":"20","author":"Friston","year":"2016","journal-title":"Trends Cogn. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Kiebel, S.J., Daunizeau, J., and Friston, K.J. (2008). A Hierarchy of Time-Scales and the Brain. PLoS Comput. Biol., 4.","DOI":"10.1371\/journal.pcbi.1000209"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"e15252","DOI":"10.7554\/eLife.15252","article-title":"A hierarchy of timescales explains distinct effects of local inhibition of primary visual cortex and frontal eye fields","volume":"5","author":"Cocchi","year":"2016","journal-title":"eLife"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1523\/JNEUROSCI.5487-07.2008","article-title":"A Hierarchy of Temporal Receptive Windows in Human Cortex","volume":"28","author":"Hasson","year":"2008","journal-title":"Off. J. Soc. Neurosci."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1038\/nn.3862","article-title":"A hierarchy of intrinsic timescales across primate cortex","volume":"17","author":"Murray","year":"2014","journal-title":"Nat. Neurosci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2226","DOI":"10.1152\/jn.1997.78.4.2226","article-title":"Object representation in the ventral premotor cortex (area F5) of the monkey","volume":"78","author":"Murata","year":"1997","journal-title":"J. Neurophysiol."},{"key":"ref_53","first-page":"473","article-title":"Auditory-Visual Integration during Multimodal Object Recognition in Humans: A Behavioral and Electrophysiological Study","volume":"11","author":"Giard","year":"1999","journal-title":"J. Neurophysiol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1152\/jn.1998.80.2.1006","article-title":"Multisensory Integration in the Superior Colliculus of the Alert Cat","volume":"80","author":"Wallace","year":"1998","journal-title":"J. Neurophysiol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2582","DOI":"10.1523\/JNEUROSCI.3987-15.2016","article-title":"Integration of Visual and Proprioceptive Limb Position Information in Human Posterior Parietal, Premotor, and Extrastriate Cortex","volume":"36","author":"Limanowski","year":"2016","journal-title":"Off. J. Soc. Neurosci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1038\/nrn2331","article-title":"Multisensory integration: Current issues from the perspective of the single neuron","volume":"9","author":"Stein","year":"2008","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"5033","DOI":"10.1073\/pnas.91.11.5033","article-title":"A measure for brain complexity: Relating functional segregation and integration in the nervous system","volume":"91","author":"Tononi","year":"1994","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1007\/s00429-017-1539-3","article-title":"Structure-function relationships during segregated and integrated network states of human brain functional connectivity","volume":"223","author":"Fukushima","year":"2018","journal-title":"Brain Struct. Funct."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1238406","DOI":"10.1126\/science.1238406","article-title":"Cortical high-density counterstream architectures","volume":"342","author":"Markov","year":"2013","journal-title":"Science"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Pearl, J. (1988). Probabilistic Reasoning. Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann.","DOI":"10.1016\/B978-0-08-051489-5.50008-4"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1098\/rstb.2008.0300","article-title":"Predictive coding under the free-energy principle","volume":"364","author":"Friston","year":"2009","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"key":"ref_62","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":"Rao","year":"1999","journal-title":"Nat. Neurosci."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1016\/j.neuroimage.2006.02.034","article-title":"Mechanisms of evoked and induced responses in MEG\/EEG","volume":"31","author":"David","year":"2006","journal-title":"NeuroImage"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.tins.2004.10.007","article-title":"The Bayesian brain: The role of uncertainty in neural coding and computation","volume":"27","author":"Knill","year":"2004","journal-title":"Trends Neurosci."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Doya, K. (2007). Bayesian Brain: Probabilistic Approaches to Neural Coding, MIT Press.","DOI":"10.7551\/mitpress\/9780262042383.001.0001"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1038\/nrn2787","article-title":"The free-energy principle: A unified brain theory?","volume":"11","author":"Friston","year":"2010","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1111\/j.1460-9568.2012.08010.x","article-title":"How can a Bayesian approach inform neuroscience?","volume":"35","author":"Jbabdi","year":"2012","journal-title":"Eur. J. Neurosci."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Tschantz, A., Seth, A.K., and Buckley, C.L. (2019). Learning action-oriented models through active inference. bioRxiv.","DOI":"10.1101\/764969"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"George, D., and Hawkins, J. (2009). Towards a mathematical theory of cortical micro-circuits. PLoS Comput. Biol., 5.","DOI":"10.1371\/journal.pcbi.1000532"},{"key":"ref_70","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":"Parr","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"20","DOI":"10.3389\/frobt.2019.00020","article-title":"Simulating Active Inference Processes by Message Passing","volume":"6","year":"2019","journal-title":"Front. Robot. AI"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"20190159","DOI":"10.1098\/rsta.2019.0159","article-title":"Markov blankets, information geometry and stochastic thermodynamics","volume":"378","author":"Parr","year":"2020","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_73","unstructured":"Sajid, N., Ball, P.J., and Friston, K.J. (2019). Demystifying active inference. arXiv."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Da Costa, L., Parr, T., Sajid, N., Veselic, S., Neacsu, V., and Friston, K. (2020). Active inference on discrete state-spaces: A synthesis. arXiv.","DOI":"10.1016\/j.jmp.2020.102447"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1111\/j.1468-2354.2007.00463.x","article-title":"Using a Laplace: Approximation to Estimate the Random Coefficients logit model by Nonlinear Least Squares*","volume":"48","author":"Harding","year":"2007","journal-title":"Int. Econ. Rev."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2089","DOI":"10.1016\/j.physd.2009.08.002","article-title":"Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models","volume":"238","author":"Daunizeau","year":"2009","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1406","DOI":"10.1109\/TKDE.2010.259","article-title":"Laplacian regularized gaussian mixture model for data clustering","volume":"23","author":"He","year":"2010","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1162\/neco_a_01102","article-title":"The Discrete and Continuous Brain: From Decisions to Movement\u2014And Back Again","volume":"30","author":"Parr","year":"2018","journal-title":"Neural Comput."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"2473","DOI":"10.1007\/s00213-019-05240-0","article-title":"The computational pharmacology of oculomotion","volume":"236","author":"Parr","year":"2019","journal-title":"Psychopharmacology"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1162\/jocn_a_00171","article-title":"The prefrontal cortex and oculomotor delayed response: A reconsideration of the \u201cmnemonic scotoma\u201d","volume":"24","author":"Tsujimoto","year":"2012","journal-title":"J. Cogn. Neurosci."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"2","DOI":"10.3389\/fnsys.2015.00002","article-title":"Functions of delay-period activity in the prefrontal cortex and mnemonic scotomas revisited","volume":"9","author":"Funahashi","year":"2015","journal-title":"Front. Syst. Neurosci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0006-8993(82)91145-3","article-title":"Delay-related activity of prefrontal neurons in rhesus monkeys performing delayed response","volume":"248","author":"Kojima","year":"1982","journal-title":"Brain Res."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"116453","DOI":"10.1016\/j.neuroimage.2019.116453","article-title":"Dynamic effective connectivity","volume":"207","author":"Zarghami","year":"2020","journal-title":"NeuroImage"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1109\/34.385979","article-title":"Tree approximations to Markov random fields","volume":"17","author":"Wu","year":"1995","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1109\/TIT.2003.810642","article-title":"Tree-based reparameterization framework for analysis of sum-product and related algorithms","volume":"49","author":"Wainwright","year":"2003","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"20130475","DOI":"10.1098\/rsif.2013.0475","article-title":"Life as we know it","volume":"10","author":"Friston","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_87","first-page":"1309","article-title":"Invariant models for causal transfer learning","volume":"19","author":"Turner","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref_88","first-page":"17","article-title":"Deep learning of representations for unsupervised and transfer learning","volume":"27","author":"Bengio","year":"2012","journal-title":"Workshop Conf. Proc."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"20141335","DOI":"10.1098\/rsif.2014.1335","article-title":"Divide et impera: Subgoaling reduces the complexity of probabilistic inference and problem solving","volume":"12","author":"Maisto","year":"2015","journal-title":"J. R. Soc. Interface"},{"key":"ref_90","first-page":"620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev. Ser. II"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1111\/nous.12062","article-title":"The Self-Evidencing Brain","volume":"50","author":"Hohwy","year":"2016","journal-title":"No\u00fbs"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/5\/552\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:28:54Z","timestamp":1760174934000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/5\/552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,14]]},"references-count":91,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["e22050552"],"URL":"https:\/\/doi.org\/10.3390\/e22050552","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,14]]}}}