{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:23:36Z","timestamp":1772173416970,"version":"3.50.1"},"reference-count":99,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MC_UU_00003\/1."],"award-info":[{"award-number":["MC_UU_00003\/1."]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>It has been suggested that the brain employs probabilistic generative models to optimally interpret sensory information. This hypothesis has been formalised in distinct frameworks, focusing on explaining separate phenomena. On one hand, classic predictive coding theory proposed how the probabilistic models can be learned by networks of neurons employing local synaptic plasticity. On the other hand, neural sampling theories have demonstrated how stochastic dynamics enable neural circuits to represent the posterior distributions of latent states of the environment. These frameworks were brought together by variational filtering that introduced neural sampling to predictive coding. Here, we consider a variant of variational filtering for static inputs, to which we refer as Monte Carlo predictive coding (MCPC). We demonstrate that the integration of predictive coding with neural sampling results in a neural network that learns precise generative models using local computation and plasticity. The neural dynamics of MCPC infer the posterior distributions of the latent states in the presence of sensory inputs, and can generate likely inputs in their absence. Furthermore, MCPC captures the experimental observations on the variability of neural activity during perceptual tasks. By combining predictive coding and neural sampling, MCPC can account for both sets of neural data that previously had been explained by these individual frameworks.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012532","type":"journal-article","created":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T13:24:47Z","timestamp":1730294687000},"page":"e1012532","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Learning probability distributions of sensory inputs with Monte Carlo predictive coding"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-6752-8296","authenticated-orcid":true,"given":"Gaspard","family":"Oliviers","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafal","family":"Bogacz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Meulemans","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,10,30]]},"reference":[{"issue":"12","key":"pcbi.1012532.ref001","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":"DC Knill","year":"2004","journal-title":"Trends in Neurosciences"},{"key":"pcbi.1012532.ref002","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/9780262042383.001.0001","volume-title":"Bayesian Brain: Probabilistic Approaches to Neural Coding","author":"K Doya","year":"2006"},{"issue":"2","key":"pcbi.1012532.ref003","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1038\/nrn2787","article-title":"The free-energy principle: a unified brain theory?","volume":"11","author":"K Friston","year":"2010","journal-title":"Nature Reviews Neuroscience"},{"issue":"6870","key":"pcbi.1012532.ref004","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1038\/415429a","article-title":"Humans integrate visual and haptic information in a statistically optimal fashion","volume":"415","author":"MO Ernst","year":"2002","journal-title":"Nature"},{"issue":"5232","key":"pcbi.1012532.ref005","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1126\/science.7569931","article-title":"An internal model for sensorimotor integration","volume":"269","author":"DM Wolpert","year":"1995","journal-title":"Science"},{"key":"pcbi.1012532.ref006","doi-asserted-by":"crossref","first-page":"12.1","DOI":"10.1167\/8.5.12","article-title":"Perceptual multistability predicted by search model for Bayesian decisions","volume":"8","author":"R Sundareswara","year":"2008","journal-title":"Journal of vision"},{"key":"pcbi.1012532.ref007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/NECO_a_00226","article-title":"Multistability and Perceptual Inference","volume":"24","author":"S Gershman","year":"2012","journal-title":"Neural computation"},{"key":"pcbi.1012532.ref008","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511984037","volume-title":"Perception as Bayesian Inference","author":"D Knill","year":"1996"},{"issue":"3","key":"pcbi.1012532.ref009","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1152\/jn.1999.81.3.1355","article-title":"Integration of proprioceptive and visual position-information: An experimentally supported model","volume":"81","author":"R van Beers","year":"1999","journal-title":"Journal of Neurophysiology"},{"key":"pcbi.1012532.ref010","volume-title":"Advances in Neural Information Processing Systems. vol. 15","author":"P Hoyer","year":"2002"},{"issue":"3","key":"pcbi.1012532.ref011","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.tics.2010.01.003","article-title":"Statistically optimal perception and learning: from behavior to neural representations","volume":"14","author":"J Fiser","year":"2010","journal-title":"Trends in Cognitive Sciences"},{"key":"pcbi.1012532.ref012","doi-asserted-by":"crossref","first-page":"12491","DOI":"10.1073\/pnas.1101430108","article-title":"Bayesian sampling in visual perception","volume":"108","author":"R Moreno-Bote","year":"2011","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"pcbi.1012532.ref013","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1038\/nn.2733","article-title":"Decoding the activity of neuronal populations in macaque primary visual cortex","volume":"14","author":"A Graf","year":"2011","journal-title":"Nature Neuroscience"},{"issue":"31","key":"pcbi.1012532.ref014","doi-asserted-by":"crossref","first-page":"10618","DOI":"10.1523\/JNEUROSCI.1335-12.2012","article-title":"A Fast and Simple Population Code for Orientation in Primate V1","volume":"32","author":"P Berens","year":"2012","journal-title":"Journal of Neuroscience"},{"issue":"6","key":"pcbi.1012532.ref015","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1016\/j.neuron.2008.09.021","article-title":"Probabilistic population codes for Bayesian decision making","volume":"60","author":"JM Beck","year":"2008","journal-title":"Neuron"},{"issue":"1","key":"pcbi.1012532.ref016","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/cercor\/1.1.1","article-title":"Distributed hierarchical processing in the primate cerebral cortex","volume":"1","author":"DJ Felleman","year":"1991","journal-title":"Cereb Cortex"},{"key":"pcbi.1012532.ref017","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1126\/science.3289116","article-title":"Localization of cognitive operations in the human brain","volume":"240","author":"MI Posner","year":"1988","journal-title":"Science"},{"issue":"1715","key":"pcbi.1012532.ref018","doi-asserted-by":"crossref","first-page":"20160260","DOI":"10.1098\/rstb.2016.0260","article-title":"Glutamatergic synapses are structurally and biochemically complex because of multiple plasticity processes: long-term potentiation, long-term depression, short-term potentiation and scaling","volume":"372","author":"J Lisman","year":"2017","journal-title":"Philos Trans R Soc Lond B Biol Sci"},{"issue":"1","key":"pcbi.1012532.ref019","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":"RP Rao","year":"1999","journal-title":"Nature Neuroscience"},{"issue":"9","key":"pcbi.1012532.ref020","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1016\/j.neunet.2003.06.005","article-title":"Learning and inference in the brain","volume":"16","author":"K Friston","year":"2003","journal-title":"Neural Networks"},{"issue":"Part B","key":"pcbi.1012532.ref021","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.jmp.2015.11.003","article-title":"A tutorial on the free-energy framework for modelling perception and learning","volume":"76","author":"R Bogacz","year":"2017","journal-title":"Journal of Mathematical Psychology"},{"issue":"1521","key":"pcbi.1012532.ref022","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":"K Friston","year":"2009","journal-title":"Philosophical Transactions of the Royal Society B: Biological Sciences"},{"issue":"1","key":"pcbi.1012532.ref023","doi-asserted-by":"crossref","first-page":"381457","DOI":"10.1155\/2009\/381457","article-title":"Unsupervised Learning of Overlapping Image Components Using Divisive Input Modulation","volume":"2009","author":"MW Spratling","year":"2009","journal-title":"Computational Intelligence and Neuroscience"},{"issue":"1205","key":"pcbi.1012532.ref024","first-page":"427","article-title":"Predictive coding: a fresh view of inhibition in the retina","volume":"216","author":"MV Srinivasan","year":"1982","journal-title":"Proceedings of the Royal Society of London Series B Biological Sciences"},{"issue":"3","key":"pcbi.1012532.ref025","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1017\/S0140525X12000477","article-title":"Whatever next? 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.1012532.ref026","article-title":"Computational psychiatry: from synapses to sentience","author":"K Friston","year":"2022","journal-title":"Molecular Psychiatry"},{"issue":"7047","key":"pcbi.1012532.ref027","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1038\/nature03689","article-title":"Dynamic predictive coding by the retina","volume":"436","author":"T Hosoya","year":"2005","journal-title":"Nature"},{"issue":"10","key":"pcbi.1012532.ref028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pbio.3000487","article-title":"Alpha oscillations and traveling waves: Signatures of predictive coding?","volume":"17","author":"A Alamia","year":"2019","journal-title":"PLOS Biology"},{"issue":"10","key":"pcbi.1012532.ref029","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1162\/neco_a_01311","article-title":"A Predictive-Coding Network That Is Both Discriminative and Generative","volume":"32","author":"W Sun","year":"2020","journal-title":"Neural Computation"},{"issue":"1","key":"pcbi.1012532.ref030","doi-asserted-by":"crossref","first-page":"2064","DOI":"10.1038\/s41467-022-29632-7","article-title":"The neural coding framework for learning generative models","volume":"13","author":"A Ororbia","year":"2022","journal-title":"Nature Communications"},{"key":"pcbi.1012532.ref031","doi-asserted-by":"crossref","first-page":"18","DOI":"10.3389\/frai.2019.00018","article-title":"The Generative Adversarial Brain","volume":"2","author":"SJ Gershman","year":"2019","journal-title":"Frontiers in Artificial Intelligence"},{"key":"pcbi.1012532.ref032","doi-asserted-by":"crossref","first-page":"e1005186","DOI":"10.1371\/journal.pcbi.1005186","article-title":"The Hamiltonian Brain: Efficient Probabilistic Inference with Excitatory-Inhibitory Neural Circuit Dynamics","volume":"12","author":"L Aitchison","year":"2016","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1012532.ref033","volume-title":"Advances in Neural Information Processing Systems. vol. 27","author":"C Savin","year":"2014"},{"issue":"8","key":"pcbi.1012532.ref034","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1162\/neco_a_01505","article-title":"Learning and Inference in Sparse Coding Models With Langevin Dynamics","volume":"34","author":"MYS Fang","year":"2022","journal-title":"Neural Computation"},{"key":"pcbi.1012532.ref035","volume-title":"Advances in Neural Information Processing Systems. vol. 22","author":"L Shi","year":"2009"},{"key":"pcbi.1012532.ref036","first-page":"1968","volume-title":"Advances in Neural Information Processing Systems 26","author":"A Grabska-Barwinska","year":"2013"},{"key":"pcbi.1012532.ref037","doi-asserted-by":"crossref","first-page":"38","DOI":"10.3389\/fncom.2014.00038","article-title":"Stochastic Variational Learning in Recurrent Spiking Networks","volume":"8","author":"D Jimenez Rezende","year":"2014","journal-title":"Front Comput Neurosci"},{"issue":"6013","key":"pcbi.1012532.ref038","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1126\/science.1195870","article-title":"Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment","volume":"331","author":"P Berkes","year":"2011","journal-title":"Science"},{"key":"pcbi.1012532.ref039","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.1012532.ref040","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1038\/s41593-020-0671-1","article-title":"Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference","volume":"23","author":"R Echeveste","year":"2020","journal-title":"Nature Neuroscience"},{"issue":"3","key":"pcbi.1012532.ref041","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/j.neuroimage.2008.03.017","article-title":"Variational filtering","volume":"41","author":"KJ Friston","year":"2008","journal-title":"NeuroImage"},{"issue":"1","key":"pcbi.1012532.ref042","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.tins.2022.09.007","article-title":"Where is the error? Hierarchical predictive coding through dendritic error computation","volume":"46","author":"FA Mikulasch","year":"2023","journal-title":"Trends in Neurosciences"},{"issue":"5","key":"pcbi.1012532.ref043","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1162\/NECO_a_00949","article-title":"An Approximation of the Error Backpropagation Algorithm in a Predictive Coding Network with Local Hebbian Synaptic Plasticity","volume":"29","author":"JCR Whittington","year":"2017","journal-title":"Neural Computation"},{"key":"pcbi.1012532.ref044","article-title":"Inferring neural activity before plasticity as a foundation for learning beyond backpropagation","author":"Y Song","year":"2024","journal-title":"Nature Neuroscience"},{"key":"pcbi.1012532.ref045","article-title":"Sequential Memory with Temporal Predictive Coding","author":"M Tang","year":"2023","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"4","key":"pcbi.1012532.ref046","doi-asserted-by":"crossref","first-page":"e1010719","DOI":"10.1371\/journal.pcbi.1010719","article-title":"Recurrent predictive coding models for associative memory employing covariance learning","volume":"19","author":"M Tang","year":"2023","journal-title":"PLoS Computational Biology"},{"key":"pcbi.1012532.ref047","unstructured":"LeCun Y, Cortes C, Burges C. MNIST handwritten digit database. ATT Labs [Online] Available: http:\/\/yannlecuncom\/exdb\/mnist. 2010;2."},{"key":"pcbi.1012532.ref048","volume-title":"Handbook of Markov Chain Monte Carlo","author":"RM Neal","year":"2010"},{"key":"pcbi.1012532.ref049","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1098\/rstb.2005.1622","article-title":"A theory of cortical responses","volume":"360","author":"K Friston","year":"2005","journal-title":"Philosophical Transactions of the Royal Society of London Series B, Biological Sciences"},{"key":"pcbi.1012532.ref050","doi-asserted-by":"crossref","DOI":"10.1142\/8195","volume-title":"The Langevin Equation","author":"WT Coffey","year":"2012","edition":"3"},{"key":"pcbi.1012532.ref051","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/978-3-030-58539-6_22","volume-title":"Computer Vision\u2013ECCV 2020","author":"E Nijkamp","year":"2020"},{"key":"pcbi.1012532.ref052","doi-asserted-by":"crossref","unstructured":"Ji X, Vedaldi A, Henriques J. Invariant Information Clustering for Unsupervised Image Classification and Segmentation. In: 2019 IEEE\/CVF International Conference on Computer Vision (ICCV). Los Alamitos, CA, USA: IEEE Computer Society; 2019. p. 9864\u20139873.","DOI":"10.1109\/ICCV.2019.00996"},{"key":"pcbi.1012532.ref053","doi-asserted-by":"crossref","unstructured":"Gavrikov P, Keuper J. CNN Filter DB: An Empirical Investigation of Trained Convolutional Filters. In: 2022 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE; 2022.","DOI":"10.1109\/CVPR52688.2022.01848"},{"key":"pcbi.1012532.ref054","unstructured":"Rezende DJ, Mohamed S, Wierstra D. Stochastic Backpropagation and Approximate Inference in Deep Generative Models. In: Proceedings of the 31st International Conference on Machine Learning. vol. 32 of Proceedings of Machine Learning Research. Bejing, China: PMLR; 2014. p. 1278\u20131286."},{"key":"pcbi.1012532.ref055","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1080\/01621459.1990.10474930","article-title":"A Monte Carlo Implementation of the EM Algorithm and the Poor Man\u2019s Data Augmentation Algorithms","volume":"85","author":"GCG Wei","year":"1990","journal-title":"Journal of the American Statistical Association"},{"key":"pcbi.1012532.ref056","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-5014-9_12","volume-title":"A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants","author":"R Neal","year":"1998"},{"key":"pcbi.1012532.ref057","unstructured":"Olshausen BA. Learning Linear, Sparse, Factorial Codes. Massachusetts Institute of Technology; 1996. AIM-1580, CBCL-138. Available from: http:\/\/hdl.handle.net\/1721.1\/7184."},{"key":"pcbi.1012532.ref058","unstructured":"Sacramento J, Costa RP, Bengio Y, Senn W. Dendritic cortical microcircuits approximate the backpropagation algorithm. In: Advances in Neural Information Processing Systems; 2018. p. 8721\u20138732."},{"key":"pcbi.1012532.ref059","unstructured":"Meulemans A, Zucchet N, Kobayashi S, von Oswald J, Sacramento Ja. The least-control principle for local learning at equilibrium. In: Advances in Neural Information Processing Systems. vol. 35. Curran Associates, Inc.; 2022. p. 33603\u201333617."},{"key":"pcbi.1012532.ref060","article-title":"GANs Trained by a Two Time-Scale Update Rule Converge to a Nash Equilibrium","author":"M Heusel","year":"2017","journal-title":"CoRR"},{"key":"pcbi.1012532.ref061","first-page":"3874","article-title":"Associative Memories via Predictive Coding","volume":"34","author":"T Salvatori","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"pcbi.1012532.ref062","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1016\/S0896-6273(03)00064-3","article-title":"Orientation and Direction Selectivity of Synaptic Inputs in Visual Cortical Neurons: A Diversity of Combinations Produces Spike Tuning","volume":"37","author":"C Monier","year":"2003","journal-title":"Neuron"},{"key":"pcbi.1012532.ref063","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.neuron.2007.02.029","article-title":"The Emergence of Contrast-Invariant Orientation Tuning in Simple Cells of Cat Visual Cortex","volume":"54","author":"IM Finn","year":"2007","journal-title":"Neuron"},{"key":"pcbi.1012532.ref064","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.neuron.2007.06.018","article-title":"Differential Attention-Dependent Response Modulation across Cell Classes in Macaque Visual Area V4","volume":"55","author":"JF Mitchell","year":"2007","journal-title":"Neuron"},{"issue":"3","key":"pcbi.1012532.ref065","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1038\/nn.2501","article-title":"Stimulus onset quenches neural variability: a widespread cortical phenomenon","volume":"13","author":"MM Churchland","year":"2010","journal-title":"Nature Neuroscience"},{"key":"pcbi.1012532.ref066","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1016\/j.neuron.2010.12.037","article-title":"Variance as a Signature of Neural Computations during Decision Making","volume":"69","author":"AK Churchland","year":"2011","journal-title":"Neuron"},{"key":"pcbi.1012532.ref067","doi-asserted-by":"crossref","first-page":"21842","DOI":"10.1073\/pnas.1009956107","article-title":"Trial-to-trial variability of the prefrontal neurons reveals the nature of their engagement in a motion discrimination task","volume":"107","author":"C Hussar","year":"2010","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1012532.ref068","doi-asserted-by":"crossref","first-page":"e43166","DOI":"10.1371\/journal.pone.0043166","article-title":"Reduced variability of ongoing and evoked cortical activity leads to improved behavioral performance","volume":"7","author":"A Ledberg","year":"2012","journal-title":"PLoS ONE"},{"key":"pcbi.1012532.ref069","doi-asserted-by":"crossref","first-page":"e41053","DOI":"10.1371\/journal.pone.0041053","article-title":"Variability of Prefrontal Neuronal Discharges before and after Training in a Working Memory Task","volume":"7","author":"XL Qi","year":"2012","journal-title":"PLoS ONE"},{"key":"pcbi.1012532.ref070","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s10955-023-03104-8","article-title":"On the Application of Non-Gaussian Noise in Stochastic Langevin Simulations","volume":"190","author":"N Gr\u00f8nbech-Jensen","year":"2023","journal-title":"Journal of Statistical Physics"},{"issue":"6","key":"pcbi.1012532.ref071","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1002\/wcs.79","article-title":"Bayesian models of cognition","volume":"1","author":"N Chater","year":"2010","journal-title":"WIREs Cognitive Science"},{"key":"pcbi.1012532.ref072","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.tics.2008.04.010","article-title":"Decision Making, Movement Planning, and Statistical Decision Theory","volume":"12","author":"J Trommersh\u00e4user","year":"2008","journal-title":"Trends in cognitive sciences"},{"issue":"48","key":"pcbi.1012532.ref073","doi-asserted-by":"crossref","first-page":"19591","DOI":"10.1073\/pnas.1308499110","article-title":"Persistence of hippocampal multivoxel patterns into postencoding rest is related to memory","volume":"110","author":"A Tambini","year":"2013","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1012532.ref074","doi-asserted-by":"crossref","first-page":"e32548","DOI":"10.7554\/eLife.32548","article-title":"Offline replay supports planning in human reinforcement learning","volume":"7","author":"I Momennejad","year":"2018","journal-title":"eLife"},{"key":"pcbi.1012532.ref075","article-title":"Generative replay for compositional visual understanding in the prefrontal-hippocampal circuit","author":"P Schwartenbeck","year":"2021","journal-title":"bioRxiv"},{"key":"pcbi.1012532.ref076","doi-asserted-by":"crossref","first-page":"15276","DOI":"10.1038\/ncomms15276","article-title":"Time-compressed preplay of anticipated events in human primary visual cortex","volume":"8","author":"M Ekman","year":"2017","journal-title":"Nature Communications"},{"issue":"6544","key":"pcbi.1012532.ref077","article-title":"Experience replay is associated with efficient nonlocal learning","volume":"372","author":"Y Liu","year":"2021","journal-title":"Science"},{"issue":"4","key":"pcbi.1012532.ref078","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/j.neuron.2012.10.038","article-title":"Canonical microcircuits for predictive coding","volume":"76","author":"AM Bastos","year":"2012","journal-title":"Neuron"},{"key":"pcbi.1012532.ref079","doi-asserted-by":"crossref","unstructured":"Millidge B, Salvatori T, Song Y, Bogacz R, Lukasiewicz T. Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation? In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI). IJCAI; 2022. p. 5538\u20135545.","DOI":"10.24963\/ijcai.2022\/774"},{"key":"pcbi.1012532.ref080","volume-title":"Advances in Neural Information Processing Systems. vol. 27","author":"G Hennequin","year":"2014"},{"key":"pcbi.1012532.ref081","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.neuron.2016.09.038","article-title":"Neural variability and sampling-based probabilistic representations in the visual cortex","volume":"92","author":"G Orb\u00e1n","year":"2016","journal-title":"Neuron"},{"key":"pcbi.1012532.ref082","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.neuron.2010.08.004","article-title":"Differences in gamma frequencies across visual cortex restrict their possible use in computation","volume":"67","author":"S Ray","year":"2010","journal-title":"Neuron"},{"key":"pcbi.1012532.ref083","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1038\/nature11665","article-title":"Inhibition dominates sensory responses in the awake cortex","volume":"493","author":"B Haider","year":"2013","journal-title":"Nature"},{"issue":"12","key":"pcbi.1012532.ref084","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1016\/j.visres.2008.03.009","article-title":"Predictive coding as a model of biased competition in visual selective attention","volume":"48","author":"MW Spratling","year":"2008","journal-title":"Vision Research"},{"issue":"4","key":"pcbi.1012532.ref085","first-page":"4","article-title":"Reconciling predictive coding and biased competition models of cortical function","volume":"2","author":"MW Spratling","year":"2008","journal-title":"Frontiers in Computational Neuroscience"},{"key":"pcbi.1012532.ref086","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2009\/381457","article-title":"Unsupervised learning of overlapping image components using divisive input modulation","volume":"2009","author":"MW Spratling","year":"2009","journal-title":"Computational Intelligence and Neuroscience"},{"issue":"4","key":"pcbi.1012532.ref087","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1011183","article-title":"Predictive coding networks for temporal prediction","volume":"20","author":"B Millidge","year":"2024","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1012532.ref088","doi-asserted-by":"crossref","unstructured":"An D, Xie J, Li P. Learning Deep Latent Variable Models by Short-Run MCMC Inference with Optimal Transport Correction. In: 2021 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR); 2021. p. 15410\u201315419.","DOI":"10.1109\/CVPR46437.2021.01516"},{"key":"pcbi.1012532.ref089","doi-asserted-by":"crossref","unstructured":"Oliviers G, Bogacz R, Meulemans A. Monte Carlo Predictive Coding: Representing the Posterior Distribution of Latent States in Predictive Coding Networks. In: Proceedings of the 2023 Conference on Cognitive Computational Neuroscience. Oxford, UK; 2023.","DOI":"10.32470\/CCN.2023.1373-0"},{"key":"pcbi.1012532.ref090","article-title":"Sample as You Infer: Predictive Coding With Langevin Dynamics","author":"U Zahid","year":"2023","journal-title":"CoRR"},{"key":"pcbi.1012532.ref091","article-title":"Neural Sampling in Hierarchical Exponential-family Energy-based Models","author":"X Dong","year":"2023","journal-title":"CoRR"},{"issue":"1","key":"pcbi.1012532.ref092","article-title":"High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm","volume":"22","author":"W Mou","year":"2021","journal-title":"J Mach Learn Res"},{"key":"pcbi.1012532.ref093","volume-title":"Advances in Neural Information Processing Systems. vol. 28","author":"YA Ma","year":"2015"},{"key":"pcbi.1012532.ref094","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1038\/nrn2258","article-title":"Noise in the nervous system","volume":"9","author":"A Faisal","year":"2008","journal-title":"Nature Reviews Neuroscience"},{"issue":"11","key":"pcbi.1012532.ref095","doi-asserted-by":"crossref","first-page":"e1003258","DOI":"10.1371\/journal.pcbi.1003258","article-title":"Predictive Coding of Dynamical Variables in Balanced Spiking Networks","volume":"9","author":"M Boerlin","year":"2013","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1012532.ref096","unstructured":"Kingma DP, Welling M. Auto-Encoding Variational Bayes. arXiv e-prints. 2013; p. arXiv:1312.6114."},{"key":"pcbi.1012532.ref097","unstructured":"Zhuo Y. Deep Latent Gaussian Models; 2019. https:\/\/github.com\/yiyuezhuo\/Deep-Latent-Gaussian-Models."},{"key":"pcbi.1012532.ref098","unstructured":"Seitzer M. pytorch-fid: FID Score for PyTorch; 2020. https:\/\/github.com\/mseitzer\/pytorch-fid."},{"key":"pcbi.1012532.ref099","doi-asserted-by":"crossref","unstructured":"P\u00e9rez-Cruz F. Kullback-Leibler Divergence Estimation of Continuous Distributions. In: 2008 IEEE International Symposium on Information Theory. IEEE; 2008. p. 1666\u20131670.","DOI":"10.1109\/ISIT.2008.4595271"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012532","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T13:25:24Z","timestamp":1730294724000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012532"}},"subtitle":[],"editor":[{"given":"Boris S.","family":"Gutkin","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2024,10,30]]},"references-count":99,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10,30]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012532","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.02.29.581455","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,30]]}}}