{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:22:57Z","timestamp":1772173377700,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012127","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000}}],"reference-count":79,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000024","name":"Canadian Institutes of Health Research","doi-asserted-by":"publisher","award":["MOP-119498"],"award-info":[{"award-number":["MOP-119498"]}],"id":[{"id":"10.13039\/501100000024","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000156","name":"Fonds de Recherche du Qu\u00e9bec - Sant\u00e9","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000156","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made additionally more difficult by cortical neurons\u2019 trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian \"map\" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The fitted models yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple\/complex nature of cells can vary in a continuous manner. We demonstrate that complex-like cells respond less reliably than simple-like cells. However, compensation for this unreliability with noise ceiling analysis reveals predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17\/18 receptive fields.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012127","type":"journal-article","created":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T16:33:46Z","timestamp":1717173226000},"page":"e1012127","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimating receptive fields of simple and complex cells in early visual cortex: A convolutional neural network model with parameterized rectification"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2163-9554","authenticated-orcid":true,"given":"Philippe","family":"Nguyen","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8135-2088","authenticated-orcid":true,"given":"Jinani","family":"Sooriyaarachchi","sequence":"additional","affiliation":[]},{"given":"Qianyu","family":"Huang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9988-3936","authenticated-orcid":true,"given":"Curtis L.","family":"Baker","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2024,5,31]]},"reference":[{"issue":"6583","key":"pcbi.1012127.ref001","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1038\/381607a0","article-title":"Emergence of simple-cell receptive field properties by learning a sparse code for natural images","volume":"381","author":"BA Olshausen","year":"1996","journal-title":"Nature"},{"issue":"1","key":"pcbi.1012127.ref002","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","article-title":"Receptive fields, binocular interaction and functional architecture in the cat\u2019s visual cortex","volume":"160","author":"DH Hubel","year":"1962","journal-title":"The Journal of physiology"},{"key":"pcbi.1012127.ref003","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1146\/annurev.neuro.29.051605.113024","article-title":"Complete functional characterization of sensory neurons by system identification","volume":"29","author":"MC Wu","year":"2006","journal-title":"Annu Rev Neurosci"},{"issue":"3","key":"pcbi.1012127.ref004","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1080\/net.12.3.289.316","article-title":"Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli","volume":"12","author":"FE Theunissen","year":"2001","journal-title":"Network"},{"issue":"5","key":"pcbi.1012127.ref005","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/j.neuron.2005.01.029","article-title":"Spatial Structure of Complex Cell Receptive Fields Measured with Natural Images","volume":"45","author":"J Touryan","year":"2005","journal-title":"Neuron"},{"key":"pcbi.1012127.ref006","first-page":"327","article-title":"Characterization of neural responses with stochastic stimuli","volume":"3","author":"EP Simoncelli","year":"2004","journal-title":"The cognitive neurosciences"},{"issue":"9","key":"pcbi.1012127.ref007","doi-asserted-by":"crossref","first-page":"e264","DOI":"10.1371\/journal.pbio.0020264","article-title":"Amplification of Trial-to-Trial Response Variability by Neurons in Visual Cortex","volume":"2","author":"M. 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