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A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011183","type":"journal-article","created":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T13:47:39Z","timestamp":1711979259000},"page":"e1011183","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":30,"title":["Predictive coding networks for temporal prediction"],"prefix":"10.1371","volume":"20","author":[{"given":"Beren","family":"Millidge","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mufeng","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahyar","family":"Osanlouy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicol S.","family":"Harper","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8994-1661","authenticated-orcid":true,"given":"Rafal","family":"Bogacz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,4,1]]},"reference":[{"key":"pcbi.1011183.ref001","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.bandc.2015.11.003","article-title":"A review of predictive coding algorithms","volume":"112","author":"MW Spratling","year":"2017","journal-title":"Brain and cognition"},{"issue":"1205","key":"pcbi.1011183.ref002","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.1011183.ref003","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF00198477","article-title":"On the computational architecture of the neocortex","volume":"66","author":"D Mumford","year":"1992","journal-title":"Biological cybernetics"},{"issue":"1","key":"pcbi.1011183.ref004","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":"1456","key":"pcbi.1011183.ref005","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 B: Biological sciences"},{"key":"pcbi.1011183.ref006","volume-title":"Surfing uncertainty: Prediction, action, and the embodied mind","author":"A Clark","year":"2015"},{"issue":"9","key":"pcbi.1011183.ref007","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"},{"key":"pcbi.1011183.ref008","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jmp.2017.09.004","article-title":"The free energy principle for action and perception: A mathematical review","volume":"81","author":"CL Buckley","year":"2017","journal-title":"Journal of Mathematical Psychology"},{"key":"pcbi.1011183.ref009","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"},{"key":"pcbi.1011183.ref010","unstructured":"Millidge B, Tschantz A, Seth A, Buckley CL. 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