Learning and inference in the brain
Abstract
This article is about how the brain data mines its sensory inputs. There are several architectural principles of functional brain anatomy that have emerged from careful anatomic and physiologic studies over the past century. These principles are considered in the light of representational learning to see if they could have been predicted a priori on the basis of purely theoretical considerations. We first review the organisation of hierarchical sensory cortices, paying special attention to the distinction between forward and backward connections. We then review various approaches to representational learning as special cases of generative models, starting with supervised learning and ending with learning based upon empirical Bayes. The latter predicts many features, such as a hierarchical cortical system, prevalent top-down backward influences and functional asymmetries between forward and backward connections that are seen in the real brain. The key points made in article are: (i). hierarchical generative models enable the learning of empirical priors and eschew prior assumptions about the causes of sensory input that are inherent in non-hierarchical models. These assumptions are necessary for learning schemes based on information theory and efficient or sparse coding, but are not necessary in a hierarchical context. Critically, the anatomical infrastructure that may implement generative models in the brain is hierarchical. Furthermore, learning based on empirical Bayes can proceed in a biologically plausible way. (ii). The second point is that backward connections are essential if the processes generating inputs cannot be inverted, or the inversion cannot be parameterised. Because these processes involve many-to-one mappings, are non-linear and dynamic in nature, they are generally non-invertible. This enforces an explicit parameterisation of generative models (i.e. backward connections) to afford recognition and suggests that forward architectures, on their own, are not sufficient for perception. (iii). Finally, non-linearities in generative models, mediated by backward connections, require these connections to be modulatory, so that representations in higher cortical levels can interact to predict responses in lower levels. This is important in relation to functional asymmetries in forward and backward connections that have been demonstrated empirically.
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This procedure combines top-down and bottom-up influences in an especially delicate and potent fashion, and leads to neurons with selectivity that is not intrinsic to the area but depends on interactions across levels of a processing hierarchy.
“This procedure combines ' top-down ' and ' bottom -up ' in fl uences in an especially delicate and potent fashion, and it leads to the development of neurons that exhibit a ' selectivity that is not intrinsic to the area but depends on interactions across levels of a processing hierarchy ' (Friston 2003, p. 1349).”
From Whatever next? Predictive brains, situated agents, and the future of cognitive science (2013) · cites this paper as Friston 2003
Grush's account of perception as 'environmental emulation' looks highly congruent with the depiction of perception as reconstructing the hidden causes structuring the sensory signal.
“In addition, Grush ' s account of perception as ' environmental emulation ' (see section 5.2 of Grush 2004) looks highly congruent with the depiction (Friston 2003 and elsewhere) of perception as reconstructing the hidden causes structuring the sensory signal.”
From Whatever next? Predictive brains, situated agents, and the future of cognitive science (2013) · cites this paper as Friston 2003
Numerous neurophysiological studies have provided evidence for signaling of prediction errors along forward connections and predictions along backward connections.
“Numerous neurophysiological studies have provided evidence for signaling of prediction errors along forward connections and predictions along backward connections [(63, 72) for reviews see (126, 127)].”
From Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice? (2016) · cites this paper as [126]
Cites
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444 · see citing works
An Information-Maximization Approach to Blind Separation and Blind Deconvolution
Bell, A. J., & Sejnowski, T. J. (1995) · Neural Computation · doi:10.1162/neco.1995.7.6.1129 · Cited by 8,986 · see citing works
Independent component analysis, A new concept?
Comon, P. (1994) · Signal Processing · doi:10.1016/0165-1684(94)90029-9 · Cited by 8,150 · see citing works
Distributed hierarchical processing in the primate cerebral cortex
Felleman, D. J., & Van Essen, D. C. (1991) · Cerebral Cortex · doi:10.1093/cercor/1.1.1 · Cited by 7,783 · see citing works
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Olshausen, B. A., & Field, D. J. (1996) · Nature · doi:10.1038/381607a0 · Cited by 5,694 · see citing works
Rao, R. P. N., & Ballard, D. H. (1999) · Nature Neuroscience · doi:10.1038/4580 · Cited by 5,483 · cited 1× · see citing works
“the nonclassical receptive field effects modelled in (Rao and Ballard, 1998)).”
BackgroundPreface: Cerebral Cortex Has Come of Age
Goldman, P. S., & RAKIC, P. T. (1991) · Cerebral Cortex · doi:10.1093/cercor/1.1.1-a · Cited by 3,412 · see citing works
Mesulam, M. (1998) · Brain · doi:10.1093/brain/121.6.1013 · Cited by 3,072 · see citing works
Nonlinear principal component analysis using autoassociative neural networks
Kramer, M. A. (1991) · AIChE Journal · doi:10.1002/aic.690370209 · Cited by 3,037 · see citing works
(1961) · Information and Control · doi:10.1016/s0019-9958(61)80064-8 · Cited by 2,904 · see citing works
Synaptic Plasticity and Memory: An Evaluation of the Hypothesis
Martin, S. J., Grimwood, P. D., & Morris, R. G. M. (2000) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.23.1.649 · Cited by 2,794 · see citing works
Functional and effective connectivity in neuroimaging: a synthesis
Friston, K. J. (1994) · Human Brain Mapping · doi:10.1002/hbm.460020107 · Cited by 2,452 · see citing works
Self-citationCATEGORY SPECIFIC SEMANTIC IMPAIRMENTS
Warrington, E. K., & Shallice, T. (1984) · Brain · doi:10.1093/brain/107.3.829 · Cited by 2,212 · see citing works
Multiple paired forward and inverse models for motor control
Wolpert, D. M., & Kawato, M. (1998) · Neural Networks · doi:10.1016/s0893-6080(98)00066-5 · Cited by 2,152 · see citing works
CORTICAL PLASTICITY: From Synapses to Maps
Buonomano, D. V., & Merzenich, M. M. (1998) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.21.1.149 · Cited by 2,083 · see citing works
Synaptic tagging and long-term potentiation
Frey, U., & Morris, R. G. M. (1997) · Nature · doi:10.1038/385533a0 · Cited by 1,736 · cited 1× · see citing works
“Schematic illustrating hierarchical structures in the brain and the distinction between forward, backward and lateral connections. the formation of synaptic 'tags' (e.g. Frey & Morris, 1997) and other calcium-dependant intracellular mechanisms.”
BackgroundSynaptic depression and cortical gain control
Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997) · Science · doi:10.1126/science.275.5297.221 · Cited by 1,690 · see citing works
Tononi, G., Sporns, O., & Edelman, G. M. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.11.5033 · Cited by 1,626 · see citing works
Computational vision and regularization theory
Poggio, T., Torre, V., & Christof Koch, A. (1985) · Nature · doi:10.1038/317314a0 · Cited by 1,414 · see citing works
A unifying computational framework for motor control and social interaction
Wolpert, D. M., Doya, K., & Kawato, M. (2003) · Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rstb.2002.1238 · Cited by 1,228 · see citing works
Dayan, P., Hinton, G. E., Neal, R. M., & Zemel, R. S. (1995) · Neural Computation · doi:10.1162/neco.1995.7.5.889 · Cited by 1,207 · see citing works
Warrington, E. K., & McCarthy, R. A. (1987) · Brain · doi:10.1093/brain/110.5.1273 · Cited by 1,125 · see citing works
Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey
Rockland, K. S., & Pandya, D. Ν. (1979) · Brain Research · doi:10.1016/0006-8993(79)90485-2 · Cited by 1,076 · see citing works
On the computational architecture of the neocortex: II The role of cortico-cortical loops
Mumford, D. (1992) · Biological Cybernetics · doi:10.1007/bf00198477 · Cited by 1,074 · see citing works
The "Wake-Sleep" Algorithm for Unsupervised Neural Networks
Hinton, G. E., Dayan, P., Frey, B. J., & Neal, R. M. (1995) · Science · doi:10.1126/science.7761831 · Cited by 1,070 · see citing works
The functional logic of cortical connections
Zeki, S., & Shipp, S. (1988) · Nature · doi:10.1038/335311a0 · Cited by 1,067 · cited 2× · see citing works
“For example, the divergence region of a point in V5 (i.e. the region receiving backward afferents from V5) may include thick and interstripes in V2 whereas its convergence region (i.e. the region providing forward afferents to V5) is limited to the thick stripes (Zeki & Shipp, 1988).”
BackgroundAttentional modulation of visual motion processing in cortical areas MT and MST
Treue, S., & Maunsell, J. H. R. (1996) · Nature · doi:10.1038/382539a0 · Cited by 1,025 · see citing works
Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Efron, B., & Morris, C. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481350 · Cited by 981 · see citing works
On the computational architecture of the neocortex: I. The role of the thalamo-cortical loop
Mumford, D. (1991) · Biological Cybernetics · doi:10.1007/bf00202389 · Cited by 929 · see citing works
Deep dyslexia: A case study of connectionist neuropsychology
Plaut, D. C., & Shallice, T. (1993) · Cognitive Neuropsychology · doi:10.1080/02643299308253469 · Cited by 853 · see citing works
NEURAL NETWORKS, PRINCIPAL COMPONENTS, AND SUBSPACES
Oja, E. (1989) · International Journal of Neural Systems · doi:10.1142/s0129065789000475 · Cited by 837 · see citing works
CATEGORY SPECIFIC ACCESS DYSPHASIA
Warrington, E. K., & McCarthy, R. A. (1983) · Brain · doi:10.1093/brain/106.4.859 · Cited by 795 · see citing works
Büchel, C. (1997) · Cerebral Cortex · doi:10.1093/cercor/7.8.768 · Cited by 794 · see citing works
Circuits for local and global signal integration in primary visual cortex
Angelucci, A., Levitt, J. B., Walton, E. J. S., Hupé, J.-M., Bullier, J., & Lund, J. S. (2002) · The Journal of Neuroscience · doi:10.1523/jneurosci.22-19-08633.2002 · Cited by 789 · see citing works
Global and fine information coded by single neurons in the temporal visual cortex
Sugase, Y., Yamane, S., Ueno, S., & Kawano, K. (1999) · Nature · doi:10.1038/23703 · Cited by 788 · see citing works
On the actions that one nerve cell can have on another: distinguishing “drivers” from “modulators”
Sherman, S. M., & Guillery, R. W. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.12.7121 · Cited by 746 · cited 1× · see citing works
“The driver can be identified as the transmitter of receptive field properties; the modulator can be identified as altering the probability of certain aspects of that transmission " (Sherman & Guillery, 1998).”
Background(1991) · Comparative Biochemistry and Physiology Part A Physiology · doi:10.1016/0300-9629(91)90509-b · Cited by 678 · see citing works
Farah, M. J., & McClelland, J. L. (1991) · Journal of Experimental Psychology General · doi:10.1037/0096-3445.120.4.339 · Cited by 670 · see citing works
Farah, M. J., & McClelland, J. L. (1991) · Journal of Experimental Psychology General · doi:10.1037//0096-3445.120.4.339 · Cited by 657 · see citing works
Lesioning an attractor network: Investigations of acquired dyslexia.
Hinton, G. E., & Shallice, T. (1991) · Psychological Review · doi:10.1037/0033-295x.98.1.74 · Cited by 656 · see citing works
Corticocortical connections in the visual system: structure and function
Salin, P. A., & Bullier, J. (1995) · Physiological Reviews · doi:10.1152/physrev.1995.75.1.107 · Cited by 639 · see citing works
Nonlinear principal component analysis—Based on principal curves and neural networks
Dong, D., & McAvoy, T. J. (1996) · Computers & Chemical Engineering · doi:10.1016/0098-1354(95)00003-k · Cited by 629 · see citing works
Neural Darwinism: selection and reentrant signaling in higher brain function.
Edelman, G. M. (1993) · Neuron · doi:10.1016/0896-6273(93)90304-a · Cited by 557 · see citing works
Towards a Theory of Early Visual Processing
Atick, J. J., & Redlich, A. (1990) · Neural Computation · doi:10.1162/neco.1990.2.3.308 · Cited by 552 · see citing works
Forming sparse representations by local anti-Hebbian learning
Földiák, P. (1990) · Biological Cybernetics · doi:10.1007/bf02331346 · Cited by 546 · see citing works
Synaptic physiology of horizontal connections in the cat's visual cortex
Hirsch, J., & Gilbert, C. (1991) · Journal of Neuroscience · doi:10.1523/jneurosci.11-06-01800.1991 · Cited by 532 · see citing works
Towards a network theory of cognition
McIntosh, A. R. (2000) · Neural Networks · doi:10.1016/s0893-6080(00)00059-9 · Cited by 500 · see citing works
Shape perception reduces activity in human primary visual cortex
Murray, S. O., Kersten, D., Olshausen, B. A., Schrater, P., & Woods, D. L. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.192579399 · Cited by 496 · see citing works
Kass, R. E., & Steffey, D. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478825 · Cited by 474 · see citing works
Beyond Phrenology: What Can Neuroimaging Tell Us About Distributed Circuitry?
Friston, K. (2002) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.25.112701.142846 · Cited by 465 · see citing works
Self-citationI NFERENCE AND C OMPUTATION WITH P OPULATION C ODES
Pouget, A., Dayan, P., & Zemel, R. S. (2003) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.26.041002.131112 · Cited by 429 · see citing works
Richmond, B. J., Optican, L. M., Podell, M., & Spitzer, H. (1987) · Journal of Neurophysiology · doi:10.1152/jn.1987.57.1.132 · Cited by 428 · see citing works
How independent are the messages carried by adjacent inferior temporal cortical neurons?
Gawne, T. J., & Richmond, B. (1993) · Journal of Neuroscience · doi:10.1523/jneurosci.13-07-02758.1993 · Cited by 425 · see citing works
Semantic memory in Alzheimer's disease.
Nebes, R. D. (1989) · Psychological Bulletin · doi:10.1037/0033-2909.106.3.377 · Cited by 423 · see citing works
A computational perspective on the neural basis of multisensory spatial representations
Pouget, A., Deneve, S., & Duhamel, J.-R. (2002) · Nature Reviews Neuroscience · doi:10.1038/nrn914 · Cited by 413 · see citing works
Optican, L. M., & Richmond, B. J. (1987) · Journal of Neurophysiology · doi:10.1152/jn.1987.57.1.162 · Cited by 380 · see citing works
Representation and separation of signals using nonlinear PCA type learning
Karhunen, J., & Joutsensalo, J. (1994) · Neural Networks · doi:10.1016/0893-6080(94)90060-4 · Cited by 374 · see citing works
Temporal dynamics of a neural solution to the aperture problem in visual area MT of macaque brain
Pack, C. C., & Born, R. T. (2001) · Nature · doi:10.1038/35059085 · Cited by 363 · see citing works
Ballard, D. H., Hinton, G. E., & Sejnowski, T. J. (1983) · Nature · doi:10.1038/306021a0 · Cited by 356 · see citing works
Constraints on cortical and thalamic projections: the no-strong-loops hypothesis
Crick, F., & Koch, C. (1998) · Nature · doi:10.1038/34584 · Cited by 353 · cited 1× · see citing works
“This is consistent with: (i) their frequent bifurcation, (ii) diffuse axonal terminations, and (iii) more divergent topography (Crick & Koch, 1998; Salin & Bullier, 1995).”
ResultIn search of common foundations for cortical computation
Phillips, W. A., & Singer, W. (1997) · Behavioral and Brain Sciences · doi:10.1017/s0140525x9700160x · Cited by 338 · see citing works
Functional integration and inference in the brain
Friston, K. J. (2002) · Progress in Neurobiology · doi:10.1016/s0301-0082(02)00076-x · Cited by 334 · see citing works
Self-citationStein's Estimation Rule and Its Competitors--An Empirical Bayes Approach
Efron, B., & Morris, C. N. (1973) · Journal of the American Statistical Association · doi:10.2307/2284155 · Cited by 331 · see citing works
Bayesian Estimation of Dynamical Systems: An Application to fMRI
Friston, K. J. (2002) · NeuroImage · doi:10.1006/nimg.2001.1044 · Cited by 310 · see citing works
Self-citationTrading spaces: Computation, representation, and the limits of uninformed learning
Clark, A., & Thornton, C. (1997) · Behavioral and Brain Sciences · doi:10.1017/s0140525x97000022 · Cited by 297 · see citing works
Information encoding and the responses of single neurons in the primate temporal visual cortex
Tovée, M. J., Rolls, E. T., Treves, A., & Bellis, R. P. (1993) · Journal of Neurophysiology · doi:10.1152/jn.1993.70.2.640 · Cited by 281 · see citing works
Coding of temporal information by activity-dependent synapses.
Fuhrmann, G., Segev, I., Markram, H., & Tsodyks, M. (2002) · Journal of Neurophysiology · doi:10.1152/jn.00258.2001 · Cited by 267 · see citing works
Perceptual Neural Organization: Some Approaches Based On Network Models And Information Theory
Linsker, R. (1990) · Annual Review of Neuroscience · doi:10.1146/annurev.ne.13.030190.001353 · Cited by 248 · see citing works
LOCALIZATION OF FUNCTION IN THE CEREBRAL CORTEX: PAST, PRESENT AND FUTURE
Phillips, C. G., Zeki, S., & Barlow, H. B. (1984) · Brain · doi:10.1093/brain/107.1.328 · Cited by 209 · see citing works
Effect of cooling area 18 on striate cortex cells in the squirrel monkey.
Sandell, J. H., & Schiller, P. H. (1982) · Journal of Neurophysiology · doi:10.1152/jn.1982.48.1.38 · Cited by 189 · see citing works
Angelucci, A., Levitt, J. B., & Lund, J. S. (2002) · Progress in brain research · doi:10.1016/s0079-6123(02)36031-x · Cited by 183 · see citing works
Visual activity in area V2 during reversible inactivation of area 17 in the macaque monkey
Girard, P., & Bullier, J. (1989) · Journal of Neurophysiology · doi:10.1152/jn.1989.62.6.1287 · Cited by 179 · see citing works
Divided by Cytochrome Oxidase: A Map of the Projections from V1 to V2 in Macaques
Sincich, L. C., & Horton, J. C. (2002) · Science · doi:10.1126/science.1067902 · Cited by 174 · see citing works
Hilgetag, C., O'Neill, M. A., & Young, M. P. (2000) · Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rstb.2000.0550 · Cited by 167 · see citing works
An optimal estimation approach to visual perception and learning
Rao, R. P. N. (1999) · Vision Research · doi:10.1016/s0042-6989(98)00279-x · Cited by 164 · see citing works
A forward-inverse optics model of reciprocal connections between visual cortical areas
Kawato, M., Hayakawa, H., & Inui, T. (1993) · Network: Computation in Neural Systems · doi:10.1088/0954-898x_4_4_001 · Cited by 151 · see citing works
Functional Organization of Speed Tuned Neurons in Visual Area MT
Liu, J., & Newsome, W. T. (2003) · Journal of Neurophysiology · doi:10.1152/jn.00097.2002 · Cited by 125 · see citing works
Early Specification of the Hierarchical Organization of Visual Cortical Areas in the Macaque Monkey
Batardière, A. (2002) · Cerebral Cortex · doi:10.1093/cercor/12.5.453 · Cited by 113 · see citing works
Motion and shape perception in cerebral akinetopsia
Rizzo, M., Nawrot, M., & Zihl, J. (1995) · Brain · doi:10.1093/brain/118.5.1105 · Cited by 101 · see citing works
Kass, R. E., & Steffey, D. L. (1989) · Journal of the American Statistical Association · doi:10.2307/2289653 · Cited by 95 · see citing works
The Inversion of Sensory Processing by Feedback Pathways: A Model of Visual Cognitive Functions
Harth, E. M., Unnikrishnan, K. P., & Pandya, A. S. (1987) · Science · doi:10.1126/science.3603015 · Cited by 92 · see citing works
Rivadulla, C., Martı́nez, L. M., Varela, C., & Cudeiro, J. (2002) · Journal of Neuroscience · doi:10.1523/jneurosci.22-07-02956.2002 · Cited by 62 · see citing works
Nonlinear PCA: characterizing interactions between modes of brain activity
Friston, K. J., Phillips, J., Chawla, D., & Büchel, C. (2000) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2000.0554 · Cited by 60 · see citing works
Self-citationAbsher, J. R., & Benson, D. F. (1993) · Neurology · doi:10.1212/wnl.43.5.862 · Cited by 59 · see citing works
Kay, J., & Phillips, W. A. (1997) · Neural Computation · doi:10.1162/neco.1997.9.4.895 · Cited by 59 · see citing works
Nonlinear source separation: the post-nonlinear mixtures.
Taleb, A., & Jutten, C. (1997) · Cited by 58 · see citing works
Principal component analysis learning algorithms: a neurobiological analysis
Friston, K. J., Frith, C., & Frackowiak, R. S. J. (1993) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.1993.0125 · Cited by 55 · see citing works
Self-citationThe motion pathways of the visual cortex
Zeki, S. (1991) · Vision · doi:10.1017/cbo9780511626197.032 · Cited by 53 · see citing works
The labile brain. III. Transients and spatio–temporal receptive fields
Friston, K. J. (2000) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2000.0562 · Cited by 37 · see citing works
Self-citationCombined physiological-anatomical approaches to study lateral inhibition
Kisvárday, Z. F., Crook, J. M., Buzás, P., et al. (2000) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(00)00299-5 · Cited by 26 · see citing works
Entropy and Cortical Activity: Information Theory and PET Findings
Friston, K. J., Frith, C., Passingham, R. E., Dolan, R. J., Liddle, P. F., & Frackowiak, R. S. J. (1992) · Cerebral Cortex · doi:10.1093/cercor/2.3.259 · Cited by 22 · see citing works
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Flagged first, then by citations
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Whatever next? Predictive brains, situated agents, and the future of cognitive science
Clark, A. (2013) · Behavioral and Brain Sciences · doi:10.1017/s0140525x12000477 · Cited by 5,924 · see citing works
A theory of cortical responses.
Friston, K. (2005) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2005.1622 · Cited by 4,578 · see citing works
Self-citationFrontal theta as a mechanism for cognitive control
Cavanagh, J. F., & Frank, M. J. (2014) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2014.04.012 · Cited by 2,726 · see citing works
Predictive coding under the free-energy principle
Friston, K., & Kiebel, S. (2009) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2008.0300 · Cited by 1,579 · see citing works
Self-citationThe mismatch negativity: a review of underlying mechanisms
Garrido, M. I., Kilner, J. M., Stephan, K. E., & Friston, K. J. (2009) · Clinical Neurophysiology · doi:10.1016/j.clinph.2008.11.029 · Cited by 1,441 · see citing works
“Hence, lower and higher areas communicate via reciprocal pathways until reconciliation; in other words, until the prediction error is suppressed and the encoding of sensory causes at higher cortical areas is optimised (Friston, 2003).”
BackgroundInfluentialSelf-citationA free energy principle for the brain
Friston, K., Kilner, J., & Harrison, L. (2006) · Journal of Physiology-Paris · doi:10.1016/j.jphysparis.2006.10.001 · Cited by 1,369 · see citing works
Self-citationThe proactive brain: using analogies and associations to generate predictions
Bar, M. (2007) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2007.05.005 · Cited by 1,144 · see citing works
Predictive coding: an account of the mirror neuron system
Kilner, J. M., Friston, K. J., & Frith, C. D. (2007) · Cognitive Processing · doi:10.1007/s10339-007-0170-2 · Cited by 1,134 · see citing works
Self-citationThe dynamic brain: from spiking neurons to neural masses and cortical fields
Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M., & Friston, K. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000092 · Cited by 1,084 · see citing works
Self-citationHierarchical Models in the Brain
Friston, K. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000211 · Cited by 952 · see citing works
“We have laid out the neurobiological and psychophysical motivation for the neuronal implementation of DEM in [3] and [4].”
Self-citationVision as Bayesian inference: analysis by synthesis?
Yuille, A., & Kersten, D. (2006) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2006.05.002 · Cited by 849 · see citing works
Synaptic plasticity and dysconnection in schizophrenia
Stephan, K. E., Baldeweg, T., & Friston, K. J. (2006) · Biological Psychiatry · doi:10.1016/j.biopsych.2005.10.005 · Cited by 841 · see citing works
Self-citationAnatomy of hierarchy: Feedforward and feedback pathways in macaque visual cortex
Markov, N. T., Vezoli, J., Chameau, P., Falchier, A., Quilodran, R., Huissoud, C., Lamy, C., Misery, P., Giroud, P., Ullman, S., et al. (2014) · Journal of Comparative Neurology · doi:10.1002/cne.23458 · Cited by 759 · see citing works
Predictions not commands: Active inference in the motor system
Adams, R. A., Shipp, S., & Friston, K. J. (2013) · Brain Structure and Function · doi:10.1007/s00429-012-0475-5 · Cited by 765 · see citing works
Self-citationFriston, K. J., & Stephan, K. E. (2007) · Synthese · doi:10.1007/s11229-007-9237-y · Cited by 673 · see citing works
Self-citationTheta lingua franca: A common mid‐frontal substrate for action monitoring processes
Cavanagh, J. F., Zambrano‐Vazquez, L., & Allen, J. J. B. (2012) · Psychophysiology · doi:10.1111/j.1469-8986.2011.01293.x · Cited by 651 · see citing works
Dynamic causal modeling of evoked responses in EEG and MEG
David, O., Kiebel, S. J., Harrison, L. M., Mattout, J., Kilner, J. M., & Friston, K. J. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2005.10.045 · Cited by 620 · see citing works
Self-citationThe default-mode, ego-functions and free-energy: a neurobiological account of Freudian ideas
Carhart-Harris, R. L., & Friston, K. J. (2010) · Brain · doi:10.1093/brain/awq010 · Cited by 574 · see citing works
Self-citationPredictive coding explains binocular rivalry: an epistemological review
Hohwy, J., Roepstorff, A., & Friston, K. (2008) · Cognition · doi:10.1016/j.cognition.2008.05.010 · Cited by 546 · see citing works
Self-citationIdentifying neural drivers with functional MRI: an electrophysiological validation
David, O., Guillemain, I., Saillet, S., Reyt, S., Deransart, C., Segebarth, C., & Depaulis, A. (2008) · PLoS Biology · doi:10.1371/journal.pbio.0060315 · Cited by 533 · see citing works
Predictive codes for forthcoming perception in the frontal cortex.
Summerfield, C., Egner, T., Greene, M., Koechlin, E., Mangels, J., & Hirsch, J. (2006) · Science · doi:10.1126/science.1132028 · Cited by 496 · see citing works
Allostatic Self-efficacy: A Metacognitive Theory of Dyshomeostasis-Induced Fatigue and Depression
Stephan, K. E., Manjaly, Z. M., Mathys, C. D., Weber, L. A. E., Paliwal, S., Gard, T., Tittgemeyer, M., Fleming, S. M., Haker, H., Seth, A. K., et al. (2016) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2016.00550 · Cited by 437 · see citing works
“The predictions by this framework suggest that differential diagnosis could be decisively facilitated by model-based estimates of directed synaptic connectivity (effective connectivity) within interoceptive circuits and their interactions with regions potentially involved in meta-cognition.”
BackgroundThe functional anatomy of the MMN: a DCM study of the roving paradigm
Garrido, M. I., Friston, K. J., Kiebel, S. J., Stephan, K. E., Baldeweg, T., & Kilner, J. M. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.05.018 · Cited by 458 · see citing works
Self-citationA critique of functional localisers
Friston, K. J., Rotshtein, P., Geng, J. J., Sterzer, P., & Henson, R. N. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2005.08.012 · Cited by 424 · see citing works
Self-citationTowards a mathematical theory of cortical micro-circuits
George, D., & Hawkins, J. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000532 · Cited by 404 · see citing works
Emotional Valence and the Free-Energy Principle
Joffily, M., & Coricelli, G. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003094 · Cited by 322 · see citing works
A Dual Role for Prediction Error in Associative Learning
den Ouden, H. E. M., Friston, K. J., Daw, N. D., McIntosh, A. R., & Stephan, K. E. (2009) · Cerebral Cortex · doi:10.1093/cercor/bhn161 · Cited by 306 · see citing works
Self-citationA ventral visual stream reading center independent of visual experience
Reich, L., Szwed, M., Cohen, L., & Amedi, A. (2011) · Current Biology · doi:10.1016/j.cub.2011.01.040 · Cited by 295 · see citing works
Evoked brain responses are generated by feedback loops
Garrido, M. I., Kilner, J. M., Kiebel, S. J., & Friston, K. J. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0706274105 · Cited by 296 · see citing works
Self-citationA tutorial on the free-energy framework for modelling perception and learning
Bogacz, R. (2017) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2015.11.003 · Cited by 283 · see citing works
Repetition suppression of faces is modulated by emotion
Ishai, A., Pessoa, L., Bikle, P. C., & Ungerleider, L. G. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0403559101 · Cited by 281 · see citing works
Uncertainty, epistemics and active inference
Parr, T., & Friston, K. J. (2017) · Journal of The Royal Society Interface · doi:10.1098/rsif.2017.0376 · Cited by 252 · see citing works
Self-citationRepetition suppression and plasticity in the human brain
Garrido, M. I., Kilner, J. M., Kiebel, S. J., Stephan, K. E., Baldeweg, T., & Friston, K. J. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.06.034 · Cited by 223 · see citing works
Self-citationThe importance of being hierarchical
Markov, N. T., & Kennedy, H. (2013) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2012.12.008 · Cited by 204 · see citing works
Petzschner, F. H., Weber, L. A. E., Gard, T., & Stephan, K. E. (2017) · Biological Psychiatry · doi:10.1016/j.biopsych.2017.05.012 · Cited by 181 · see citing works
A review of gaze entropy as a measure of visual scanning efficiency
Shiferaw, B., Downey, L., & Crewther, D. (2019) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2018.12.007 · Cited by 203 · see citing works
Fenske, M. J., Aminoff, E., Gronau, N., & Bar, M. (2006) · Progress in brain research · doi:10.1016/s0079-6123(06)55001-0 · Cited by 190 · see citing works
Dikker, S., Silbert, L. J., Hasson, U., & Zevin, J. D. (2014) · The Journal of Neuroscience · doi:10.1523/jneurosci.3796-13.2014 · Cited by 167 · see citing works
Modelling trial-by-trial changes in the mismatch negativity
Lieder, F., Daunizeau, J., Garrido, M. I., Friston, K. J., & Stephan, K. E. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002911 · Cited by 168 · see citing works
Prediction, Bayesian inference and feedback in speech recognition
Norris, D., McQueen, J. M., & Cutler, A. (2016) · Language, Cognition and Neuroscience · doi:10.1080/23273798.2015.1081703 · Cited by 170 · see citing works
Predictive processing as a systematic basis for identifying the neural correlates of consciousness
Hohwy, J., & Seth, A. (2020) · Philosophy and the Mind Sciences · doi:10.33735/phimisci.2020.ii.64 · Cited by 170 · see citing works
Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?
Haker, H., Schneebeli, M., & Stephan, K. E. (2016) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2016.00107 · Cited by 130 · see citing works
Interactive Activation and Mutual Constraint Satisfaction in Perception and Cognition
McClelland, J. L., Mirman, D., Bolger, D. J., & Khaitan, P. (2014) · Cognitive Science · doi:10.1111/cogs.12146 · Cited by 122 · see citing works
Impaired top-down processes in schizophrenia: a DCM study of ERPs
Dima, D., Dietrich, D. E., Dillo, W., & Emrich, H. M. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.12.086 · Cited by 122 · see citing works
Mistaking a house for a face: neural correlates of misperception in healthy humans
Summerfield, C., Egner, T., Mangels, J., & Hirsch, J. (2006) · Cerebral Cortex · doi:10.1093/cercor/bhi129 · Cited by 120 · see citing works
Deep active inference as variational policy gradients
Millidge, B. (2020) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2020.102348 · Cited by 115 · see citing works
Forward and backward connections in the brain: a DCM study of functional asymmetries
Chen, C. C., Henson, R. N., Stephan, K. E., Kilner, J. M., & Friston, K. J. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2008.12.041 · Cited by 109 · see citing works
Baldeweg, T., & Hirsch, S. R. (2015) · International Journal of Psychophysiology · doi:10.1016/j.ijpsycho.2014.03.008 · Cited by 108 · 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
First principles in the life sciences: the free-energy principle, organicism, and mechanism
Colombo, M., & Wright, C. (2021) · Synthese · doi:10.1007/s11229-018-01932-w · Cited by 101 · see citing works
Smooth pursuit and visual occlusion: active inference and oculomotor control in schizophrenia
Adams, R. A., Perrinet, L. U., & Friston, K. (2012) · PLoS ONE · doi:10.1371/journal.pone.0047502 · Cited by 91 · see citing works
Self-citationPredictive Coding Approximates Backprop Along Arbitrary Computation Graphs
Millidge, B., Tschantz, A., & Buckley, C. L. (2022) · Neural Computation · doi:10.1162/neco_a_01497 · Cited by 95 · see citing works
Allostasis, action and affect in depression: Insights from the theory of constructed emotion
Shaffer, C., Westlin, C., Quigley, K. S., Whitfield-Gabrieli, S., & Barrett, L. F. (2022) · Annual Review of Clinical Psychology · doi:10.1146/annurev-clinpsy-081219-115627 · Cited by 94 · see citing works
Extra-classical receptive field effects measured in striate cortex with fMRI
Harrison, L. M., Stephan, K. E., Rees, G., & Friston, K. J. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2006.10.017 · Cited by 89 · see citing works
Self-citationSensitivity to pain expectations: A Bayesian model of individual differences
Hoskin, R., Berzuini, C., Acosta-Kane, D., El-Deredy, W., Guo, H., & Talmi, D. (2019) · Cognition · doi:10.1016/j.cognition.2018.08.022 · Cited by 87 · see citing works
Brown, C. A., Seymour, B., El-Deredy, W., & Jones, A. K. P. (2008) · Pain · doi:10.1016/j.pain.2008.04.028 · Cited by 83 · see citing works
A Bayesian Perspective on Sensory and Cognitive Integration in Pain Perception and Placebo Analgesia
Anchisi, D., & Zanon, M. (2015) · PLOS ONE · doi:10.1371/journal.pone.0117270 · Cited by 84 · see citing works
The empirical status of predictive coding and active inference
Hodson, R., Mehta, M., & Smith, R. (2024) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2023.105473 · Cited by 69 · see citing works
Kwisthout, J., Bekkering, H., & van Rooij, I. (2017) · Brain and Cognition · doi:10.1016/j.bandc.2016.02.008 · Cited by 73 · see citing works
Mismatch negativity (MMN) as a tool for translational investigations into early psychosis: A review
Tada, M., Kirihara, K., Mizutani, S., Uka, T., Kunii, N., Koshiyama, D., Fujioka, M., Usui, K., Nagai, T., Araki, T., et al. (2019) · International Journal of Psychophysiology · doi:10.1016/j.ijpsycho.2019.02.009 · Cited by 74 · see citing works
Evolutionary systems theory: a unifying meta-theory of psychological science
Badcock, P. B. (2012) · Review of General Psychology · doi:10.1037/a0026381 · Cited by 61 · see citing works
Williams, D. (2020) · Synthese · doi:10.1007/s11229-018-1768-x · Cited by 63 · see citing works
Why should any body have a self?
Hohwy, J., & Michael, J. (2017) · doi:10.31234/osf.io/fm4cr · Cited by 54 · see citing works
Affective experience in the predictive mind: a review and new integrative account
Fernandez Velasco, P., & Loev, S. (2021) · Synthese · doi:10.1007/s11229-020-02755-4 · Cited by 43 · see citing works
Butz, M. V. (2021) · KI - Künstliche Intelligenz · doi:10.1007/s13218-021-00705-x · Cited by 42 · see citing works
Neural correlates of hierarchical predictive processes in autistic adults
Sapey-Triomphe, L.-A., Pattyn, L., Weilnhammer, V., Sterzer, P., & Wagemans, J. (2023) · Nature Communications · doi:10.1038/s41467-023-38580-9 · Cited by 35 · see citing works
Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?
Millidge, B., Salvatori, T., Song, Y., Bogacz, R., & Lukasiewicz, T. (2022) · arXiv · doi:10.48550/arxiv.2202.09467 · Cited by 31 · see citing works
Interpersonal Motor Interactions Shape Multisensory Representations of the Peripersonal Space
Fanghella, M., Era, V., & Candidi, M. (2021) · Brain Sciences · doi:10.3390/brainsci11020255 · Cited by 22 · see citing works
Species of realization and the free energy principle
Kirchhoff, M. D. (2015) · Australasian Journal of Philosophy · doi:10.1080/00048402.2014.992446 · Cited by 19 · see citing works
The Free Energy Principle: Good Science and Questionable Philosophy in a Grand Unifying Theory
Sánchez-Cañizares, J. (2021) · Entropy · doi:10.3390/e23020238 · Cited by 16 · see citing works
Gendron, M., Mesquita, B., & Barrett, L. F. (2020) · Culture, Mind, and Brain · doi:10.1017/9781108695374.010 · Cited by 20 · see citing works
Schizophrenia, Subjectivity, and Mindreading
Nour, M. M., & Barrera, A. (2015) · Schizophrenia Bulletin · doi:10.1093/schbul/sbv035 · Cited by 10 · see citing works
A survey on neuro-mimetic deep learning via predictive coding
Salvatori, T., Mali, A., Buckley, C. L., Lukasiewicz, T., Rao, R. P. N., Friston, K., & Ororbia, A. (2026) · Neural Networks · doi:10.1016/j.neunet.2025.108161 · Cited by 2 · see citing works
Self-citation
- Authors
- Friston, K.
- Affiliations
- UCL Queen Square Institute of Neurology (GB)
- Corresponding author
- Friston, Karl
- ORCID
- Friston, Karl
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 2003-11
- Volume
- 16
- Issue
- 9
- Pages
- 1325-1352
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2131352719
- Cited by
- 724
- References
- 91
- Citations by year
- 2026: 26 · 2025: 51 · 2024: 34 · 2023: 52 · 2022: 51 · 2021: 60 · 2020: 83 · 2019: 33 · 2018: 38 · 2017: 36 · 2016: 25 · 2015: 31 · 2014: 24 · 2013: 26 · 2012: 23
- FWCI
- 4.56
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- representation learning, generative models, top-down connections, empirical Bayes, empirical priors, functional asymmetry, sparse coding, efficient coding, information theory, perception, brain architecture
- MeSH terms
- Bayes Theorem, Brain, Learning, Neural Networks, Computer
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