Free-energy and the brain

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 inputs 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.

[1]  Rajesh P. N. Rao,et al.  Bayesian inference and attentional modulation in the visual cortex , 2005, Neuroreport.

[2]  P. Goldman-Rakic,et al.  Preface: Cerebral Cortex Has Come of Age , 1991 .

[3]  P. Cz. Handbuch der physiologischen Optik , 1896 .

[4]  Karl J. Friston,et al.  Dynamic representations and generative models of brain function , 2001, Brain Research Bulletin.

[5]  Michael I. Jordan Learning in Graphical Models , 1999, NATO ASI Series.

[6]  Erkki Oja,et al.  Neural Networks, Principal Components, and Subspaces , 1989, Int. J. Neural Syst..

[7]  Daniel A. Levinthal,et al.  Exploration and Exploitation in Organizational Learning , 2007 .

[8]  Geoffrey E. Hinton,et al.  The Helmholtz Machine , 1995, Neural Computation.

[9]  L Krubitzer,et al.  Area 3a: topographic organization and cortical connections in marmoset monkeys. , 2001, Cerebral cortex.

[10]  Debra J. Searles,et al.  The Fluctuation Theorem , 2002 .

[11]  Angela J. Yu,et al.  Uncertainty, Neuromodulation, and Attention , 2005, Neuron.

[12]  Huzihiro Araki,et al.  Quantum and Non-Commutative Analysis , 1993 .

[13]  John H. R. Maunsell,et al.  Attentional modulation of visual motion processing in cortical areas MT and MST , 1996, Nature.

[14]  Karl J. Friston Learning and inference in the brain , 2003, Neural Networks.

[15]  R. F. Streater The Free-energy Theorem , 1993 .

[16]  A Prince,et al.  Optimality: From Neural Networks to Universal Grammar , 1997, Science.

[17]  Christopher C. Pack,et al.  Temporal dynamics of a neural solution to the aperture problem in visual area MT of macaque brain , 2001, Nature.

[18]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[19]  Paul Schrater,et al.  Shape perception reduces activity in human primary visual cortex , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[20]  G. Edelman Neural Darwinism: Selection and reentrant signaling in higher brain function , 1993, Neuron.

[21]  M. Mesulam,et al.  From sensation to cognition. , 1998, Brain : a journal of neurology.

[22]  R Linsker,et al.  Perceptual neural organization: some approaches based on network models and information theory. , 1990, Annual review of neuroscience.

[23]  Panos E. Trahanias,et al.  Modelling brain emergent behaviours through coevolution of neural agents , 2006, Neural Networks.

[24]  Rajesh P. N. Rao,et al.  Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. , 1999 .

[25]  P. Klouček,et al.  The computational modeling of nonequilibrium thermodynamics of the martensitic transformations , 1998 .

[26]  B. Efron,et al.  Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach , 1973 .

[27]  E Harth,et al.  The inversion of sensory processing by feedback pathways: a model of visual cognitive functions. , 1987, Science.

[28]  M. Young,et al.  Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac). , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[29]  G. Orban,et al.  Laminar distribution of NMDA receptors in cat and monkey visual cortex visualized by [3H]‐MK‐801 binding , 1993, The Journal of comparative neurology.

[30]  G. Crooks Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  J. B. Levitt,et al.  Anatomical origins of the classical receptive field and modulatory surround field of single neurons in macaque visual cortical area V1. , 2002, Progress in brain research.

[32]  Shihui Han,et al.  Modulation of neural activities by enhanced local selection in the processing of compound stimuli , 2003, Human brain mapping.

[33]  J. M. Hupé,et al.  Cortical feedback improves discrimination between figure and background by V1, V2 and V3 neurons , 1998, Nature.

[34]  D. Mackay The Epistemological Problem for Automata , 1956 .

[35]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[36]  Karl J. Friston,et al.  DEM: A variational treatment of dynamic systems , 2008, NeuroImage.

[37]  D Mumford,et al.  On the computational architecture of the neocortex. II. The role of cortico-cortical loops. , 1992, Biological cybernetics.

[38]  Denis J. Evans,et al.  A non-equilibrium free energy theorem for deterministic systems , 2003 .

[39]  H. Spitzer,et al.  Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. I. Response characteristics. , 1987, Journal of neurophysiology.

[40]  C. Gilbert,et al.  Synaptic physiology of horizontal connections in the cat's visual cortex , 1991, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[41]  R. Kass,et al.  Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models) , 1989 .

[42]  Geoffrey E. Hinton,et al.  Parallel visual computation , 1983, Nature.

[43]  A. Dale,et al.  Human posterior auditory cortex gates novel sounds to consciousness. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[44]  S. Shipp,et al.  The functional logic of cortical connections , 1988, Nature.

[45]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[46]  Mitsuo Kawato,et al.  A forward-inverse optics model of reciprocal connections between visual cortical areas , 1993 .

[47]  Geoffrey E. Hinton,et al.  Keeping the neural networks simple by minimizing the description length of the weights , 1993, COLT '93.

[48]  Pierre Baldi,et al.  Bayesian surprise attracts human attention , 2005, Vision Research.

[49]  R. Andersen Visual and eye movement functions of the posterior parietal cortex. , 1989, Annual review of neuroscience.

[50]  D A Pollen,et al.  On the neural correlates of visual perception. , 1999, Cerebral cortex.

[51]  Tai Sing Lee,et al.  Hierarchical Bayesian inference in the visual cortex. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[52]  D. Mackay Free energy minimisation algorithm for decoding and cryptanalysis , 1995 .

[53]  D. Mumford On the computational architecture of the neocortex , 2004, Biological Cybernetics.

[54]  J. DeFelipe,et al.  Microstructure of the neocortex: Comparative aspects , 2002, Journal of neurocytology.

[55]  Karl J. Friston,et al.  Variational free energy and the Laplace approximation , 2007, NeuroImage.

[56]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[57]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[58]  Konrad Paul Kording,et al.  Bayesian integration in sensorimotor learning , 2004, Nature.

[59]  Joseph J. Atick,et al.  Towards a Theory of Early Visual Processing , 1990, Neural Computation.

[60]  P. Földiák,et al.  Forming sparse representations by local anti-Hebbian learning , 1990, Biological Cybernetics.

[61]  John J. Foxe,et al.  Determinants and mechanisms of attentional modulation of neural processing. , 2001, Frontiers in Bioscience.

[62]  R. Guillery,et al.  On the actions that one nerve cell can have on another: distinguishing "drivers" from "modulators". , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[63]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[64]  L. Optican,et al.  Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis. , 1987, Journal of neurophysiology.

[65]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[66]  A. Clark,et al.  Trading spaces: Computation, representation, and the limits of uninformed learning , 1997, Behavioral and Brain Sciences.

[67]  S. Treue,et al.  Feature-Based Attention Increases the Selectivity of Population Responses in Primate Visual Cortex , 2004, Current Biology.

[68]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[69]  J. B. Levitt,et al.  Circuits for Local and Global Signal Integration in Primary Visual Cortex , 2002, The Journal of Neuroscience.

[70]  P. C. Murphy,et al.  Corticofugal feedback influences the generation of length tuning in the visual pathway , 1987, Nature.

[71]  久保 亮五,et al.  H. Haken: Synergetics; An Introduction Non-equilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology, Springer-Verlag, Berlin and Heidelberg, 1977, viii+325ページ, 251×17.5cm, 11,520円. , 1978 .

[72]  H. Morowitz,et al.  Energy Flow in Biology , 1969 .

[73]  T. Shallice,et al.  Neuroimaging evidence for dissociable forms of repetition priming. , 2000, Science.

[74]  W. Singer,et al.  In search of common foundations for cortical computation , 1997, Behavioral and Brain Sciences.

[75]  S. Hochstein,et al.  View from the Top Hierarchies and Reverse Hierarchies in the Visual System , 2002, Neuron.

[76]  Roman Borisyuk,et al.  A theory of epineuronal memory , 2004, Neural Networks.

[77]  R. Näätänen Mismatch negativity: clinical research and possible applications. , 2003, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[78]  K. Rockland,et al.  Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey , 1979, Brain Research.

[79]  A. Yuille,et al.  Object perception as Bayesian inference. , 2004, Annual review of psychology.

[80]  D. Harville Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[81]  Karl J. Friston,et al.  A theory of cortical responses , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[82]  Geoffrey E. Hinton,et al.  A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants , 1998, Learning in Graphical Models.