{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T11:50:07Z","timestamp":1773748207747,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010270","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T00:00:00Z","timestamp":1659398400000}}],"reference-count":58,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Amidex","award":["AMX-19-IET-004"],"award-info":[{"award-number":["AMX-19-IET-004"]}]},{"name":"ANR","award":["ANR-17-EURE-0029"],"award-info":[{"award-number":["ANR-17-EURE-0029"]}]},{"name":"ANR","award":["ANR-10-EQPX-29-01"],"award-info":[{"award-number":["ANR-10-EQPX-29-01"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of orientation maps in higher mammals\u2019 V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a theoretical model based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence in V1 of complex cells with or without that of orientation maps, as observed in distinct species of mammals. In particular, we observed that pooling in the feature space is directly related to the orientation map formation while pooling in the retinotopic space is responsible for the emergence of a complex cells population. Introducing different forms of pooling in a predictive model of early visual processing as implemented in SDPC can therefore be viewed as a theoretical framework that explains the diversity of structural and functional phenomena observed in V1.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010270","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T14:03:58Z","timestamp":1658412238000},"page":"e1010270","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Pooling strategies in V1 can account for the functional and structural diversity across 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Antol\u00edk","year":"2011","journal-title":"Frontiers in Computational Neuroscience"},{"issue":"11","key":"pcbi.1010270.ref027","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1162\/neco_a_01325","article-title":"Effect of top-down connections in Hierarchical Sparse Coding","volume":"32","author":"V Boutin","year":"2020","journal-title":"Neural Computation"},{"issue":"1","key":"pcbi.1010270.ref028","doi-asserted-by":"crossref","first-page":"e1008629","DOI":"10.1371\/journal.pcbi.1008629","article-title":"Sparse deep predictive coding captures contour integration capabilities of the early visual system","volume":"17","author":"V Boutin","year":"2021","journal-title":"PLoS computational biology"},{"key":"pcbi.1010270.ref029","first-page":"217","article-title":"Possible principles underlying the transformation of sensory messages","volume":"1","author":"HB Barlow","year":"1961","journal-title":"Sensory 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Neurology"},{"issue":"3","key":"pcbi.1010270.ref049","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1002\/cne.901880305","article-title":"The rabbit and the cat: a comparison of some features of response properties of single cells in the primary visual cortex","volume":"188","author":"EH Murphy","year":"1979","journal-title":"Journal of Comparative Neurology"},{"issue":"1","key":"pcbi.1010270.ref050","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0896-6273(01)00570-0","article-title":"Opponent inhibition: A developmental model of layer 4 of the neocortical circuit","volume":"33","author":"AS Kayser","year":"2002","journal-title":"Neuron"},{"issue":"7","key":"pcbi.1010270.ref051","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1162\/NECO_a_00843","article-title":"Learning visual spatial pooling by strong PCA dimension reduction","volume":"28","author":"H Hosoya","year":"2016","journal-title":"Neural computation"},{"key":"pcbi.1010270.ref052","doi-asserted-by":"crossref","first-page":"18","DOI":"10.3389\/fncom.2019.00018","article-title":"Deep learning with asymmetric connections and Hebbian updates","volume":"13","author":"Y Amit","year":"2019","journal-title":"Frontiers in computational neuroscience"},{"issue":"5","key":"pcbi.1010270.ref053","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":"JC Whittington","year":"2017","journal-title":"Neural computation"},{"key":"pcbi.1010270.ref054","unstructured":"Boutin V, Zerroug A, Jung M, Serre T. Iterative VAE as a predictive brain model for out-of-distribution generalization. arXiv preprint arXiv:201200557. 2020;."},{"key":"pcbi.1010270.ref055","unstructured":"Coates A, Ng A, Lee H. An analysis of single-layer networks in unsupervised feature learning. In: Proceedings of the fourteenth international conference on artificial intelligence and statistics; 2011. p. 215\u2013223."},{"issue":"6","key":"pcbi.1010270.ref056","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF00354980","article-title":"Quantitative determination of orientational and directional components in the response of visual cortical cells to moving stimuli","volume":"57","author":"F W\u00f6rg\u00f6tter","year":"1987","journal-title":"Biological cybernetics"},{"issue":"2","key":"pcbi.1010270.ref057","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11263-006-0026-8","article-title":"Self-Invertible 2D Log-Gabor Wavelets","volume":"75","author":"S Fischer","year":"2007","journal-title":"International Journal of Computer Vision"},{"issue":"1","key":"pcbi.1010270.ref058","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s004220050411","article-title":"Orientation tuning curves: empirical description and estimation of parameters","volume":"78","author":"NV Swindale","year":"1998","journal-title":"Biological cybernetics"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010270","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T00:00:00Z","timestamp":1659398400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T15:21:29Z","timestamp":1659453689000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010270"}},"subtitle":[],"editor":[{"given":"Saad","family":"Jbabdi","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,7,21]]},"references-count":58,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7,21]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010270","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.04.19.440444","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,21]]}}}