{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T18:55:13Z","timestamp":1777661713919,"version":"3.51.4"},"reference-count":59,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T00:00:00Z","timestamp":1613088000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Skilled behavior often displays signatures of Bayesian inference. In order for the brain to implement the required computations, neuronal activity must carry accurate information about the uncertainty of sensory inputs. Two major approaches have been proposed to study neuronal representations of uncertainty. The first one, the Bayesian decoding approach, aims primarily at decoding the posterior probability distribution of the stimulus from population activity using Bayes\u2019 rule, and indirectly yields uncertainty estimates as a by-product. The second one, which we call the correlational approach, searches for specific features of neuronal activity (such as tuning-curve width and maximum firing-rate) which correlate with uncertainty. To compare these two approaches, we derived a new normative model of sound source localization by Interaural Time Difference (ITD), that reproduces a wealth of behavioral and neural observations. We found that several features of neuronal activity correlated with uncertainty on average, but none provided an accurate estimate of uncertainty on a trial-by-trial basis, indicating that the correlational approach may not reliably identify which aspects of neuronal responses represent uncertainty. In contrast, the Bayesian decoding approach reveals that the activity pattern of the entire population was required to reconstruct the trial-to-trial posterior distribution with Bayes\u2019 rule. These results suggest that uncertainty is unlikely to be represented in a single feature of neuronal activity, and highlight the importance of using a Bayesian decoding approach when exploring the neural basis of uncertainty.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008138","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T21:11:19Z","timestamp":1613164279000},"page":"e1008138","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":17,"title":["Investigating the representation of uncertainty in neuronal circuits"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7522-8785","authenticated-orcid":true,"given":"Guillaume P.","family":"Dehaene","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2052-5894","authenticated-orcid":true,"given":"Ruben","family":"Coen-Cagli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3054-6365","authenticated-orcid":true,"given":"Alexandre","family":"Pouget","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,2,12]]},"reference":[{"key":"pcbi.1008138.ref001","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511984037","author":"D. 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Saberi","year":"1998","journal-title":"Neuron"},{"key":"pcbi.1008138.ref018","doi-asserted-by":"crossref","first-page":"e7721","DOI":"10.1371\/journal.pone.0007721","article-title":"Improvements of sound localization abilities by the facial ruff of the barn owl (Tyto alba) as demonstrated by virtual ruff removal","volume":"4","author":"L. Hausmann","year":"2009","journal-title":"PLoS One"},{"key":"pcbi.1008138.ref019","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1038\/nn.3495","article-title":"Probabilistic brains: knowns and unknowns","volume":"16","author":"A. Pouget","year":"2013","journal-title":"Nat Neurosci"},{"key":"pcbi.1008138.ref020","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1037\/h0061495","article-title":"A place theory of sound localization","volume":"41","author":"L. A. Jeffress","year":"1948","journal-title":"Journal of comparative and physiological psychology"},{"key":"pcbi.1008138.ref021","doi-asserted-by":"crossref","first-page":"3227","DOI":"10.1523\/JNEUROSCI.10-10-03227.1990","article-title":"A circuit for detection of interaural time differences in the brain stem of the barn owl","volume":"10","author":"C. Carr","year":"1990","journal-title":"The Journal of Neuroscience"},{"key":"pcbi.1008138.ref022","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1038\/86049","article-title":"A neural code for low-frequency sound localization in mammals","volume":"4","author":"D. McAlpine","year":"2001","journal-title":"Nature neuroscience"},{"key":"pcbi.1008138.ref023","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1152\/jn.1990.64.2.465","article-title":"Interaural time sensitivity in medial superior olive of cat","volume":"64","author":"T. Yin","year":"1990","journal-title":"Journal of neurophysiology"},{"key":"pcbi.1008138.ref024","first-page":"15310","article-title":"Marginalization in neural circuits with divisive normalization. The Journal of neuroscience: the official journal of the","volume":"31","author":"J. M. Beck","year":"2011","journal-title":"Society for Neuroscience"},{"key":"pcbi.1008138.ref025","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.tics.2012.08.010","article-title":"Organizing probabilistic models of perception","volume":"16","author":"W. J. Ma","year":"2012","journal-title":"Trends in Cognitive Sciences"},{"key":"pcbi.1008138.ref026","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1523\/JNEUROSCI.02-09-01177.1982","article-title":"Auditory and visual maps of space in the optic tectum of the owl","volume":"2","author":"E. I. Knudsen","year":"1982","journal-title":"The Journal of Neuroscience"},{"key":"pcbi.1008138.ref027","doi-asserted-by":"crossref","DOI":"10.1523\/ENEURO.0144-17.2017","article-title":"Distinct Correlation Structure Supporting a Rate-Code for Sound Localization in the Owl's Auditory Forebrain","volume":"4","author":"M. V. Beckert","year":"2017","journal-title":"eNeuro"},{"key":"pcbi.1008138.ref028","doi-asserted-by":"crossref","first-page":"E6973","DOI":"10.1073\/pnas.1508738112","article-title":"Origin of information-limiting noise correlations","volume":"112","author":"I. Kanitscheider","year":"2015","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1008138.ref029","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.neuron.2015.09.039","article-title":"Confidence as Bayesian Probability: From Neural Origins to Behavior","volume":"88","author":"F. Meyniel","year":"2015","journal-title":"Neuron"},{"key":"pcbi.1008138.ref030","volume-title":"Deep learning","author":"I. Goodfellow","year":"2016"},{"key":"pcbi.1008138.ref031","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1038\/nn.4150","article-title":"Sensory uncertainty decoded from visual cortex predicts behavior","volume":"18","author":"R. S. Van Bergen","year":"2015","journal-title":"Nature neuroscience"},{"key":"pcbi.1008138.ref032","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. B. Graf","year":"2011","journal-title":"Nature neuroscience"},{"key":"pcbi.1008138.ref033","first-page":"10618","article-title":"A fast and simple population code for orientation in primate V1. The Journal of neuroscience: the official journal of the","volume":"32","author":"P. Berens","year":"2012","journal-title":"Society for Neuroscience"},{"key":"pcbi.1008138.ref034","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1038\/nn1792","article-title":"Optimal decoding of correlated neural population responses in the primate visual cortex","volume":"9","author":"Y. Chen","year":"2006","journal-title":"Nature neuroscience"},{"key":"pcbi.1008138.ref035","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1523\/JNEUROSCI.3449-12.2013","article-title":"Adaptation improves neural coding efficiency despite increasing correlations in variability","volume":"33","author":"M. Adibi","year":"2013","journal-title":"The Journal of Neuroscience"},{"key":"pcbi.1008138.ref036","article-title":"Decoding subjective decisions from orbitofrontal cortex","author":"E. L. 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Adelson","year":"1985","journal-title":"JOSA A"},{"key":"pcbi.1008138.ref041","first-page":"81","article-title":"Velocity likelihoods in biological and machine vision","author":"Y. Weiss","year":"2002","journal-title":"Probabilistic models of the brain: Perception and neural function"},{"key":"pcbi.1008138.ref042","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1167\/14.2.1","article-title":"Optimal disparity estimation in natural stereo images","volume":"14","author":"J. Burge","year":"2014","journal-title":"Journal of vision"},{"key":"pcbi.1008138.ref043","doi-asserted-by":"crossref","DOI":"10.1038\/ncomms8900","article-title":"Optimal speed estimation in natural image movies predicts human performance","volume":"6","author":"J. Burge","year":"2015","journal-title":"Nature communications"},{"key":"pcbi.1008138.ref044","doi-asserted-by":"crossref","first-page":"051904","DOI":"10.1103\/PhysRevE.64.051904","article-title":"Population coding in neuronal systems with correlated noise","volume":"64","author":"H. Sompolinsky","year":"2001","journal-title":"Physical Review E"},{"key":"pcbi.1008138.ref045","first-page":"14272","article-title":"The effect of noise correlations in populations of diversely tuned neurons. The Journal of neuroscience: the official journal of the","volume":"31","author":"A. S. Ecker","year":"2011","journal-title":"Society for Neuroscience"},{"key":"pcbi.1008138.ref046","doi-asserted-by":"crossref","DOI":"10.1146\/annurev-neuro-070815-013851","article-title":"Correlations and neuronal population information","volume":"39","author":"A. Kohn","year":"2016","journal-title":"Annual review of neuroscience"},{"key":"pcbi.1008138.ref047","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1038\/nn.3711","article-title":"Partitioning neuronal variability","volume":"17","author":"R. L. Goris","year":"2014","journal-title":"Nature neuroscience"},{"key":"pcbi.1008138.ref048","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.neuron.2014.02.006","article-title":"State dependence of noise correlations in macaque primary visual cortex","volume":"82","author":"A. S. Ecker","year":"2014","journal-title":"Neuron"},{"key":"pcbi.1008138.ref049","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1038\/nn.4242","article-title":"The mechanics of state-dependent neural correlations","volume":"19","author":"B. 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