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Simulations show that using these operations, a large-scale circuit, which combines populations of spiking neurons as basic building blocks, is capable of finding close approximations to the full mathematical computations performed by graphical models within a few hundred milliseconds. The circuit is general in the sense that it can be wired for any graph structure, it supports multistate variables, and it uses standard leaky integrate-and-fire neuronal units. Following previous work, which proposed relations between graphical models and the large-scale cortical anatomy, we focus on the cortical microcircuitry and propose how anatomical and physiological aspects of the local circuitry may map onto elements of the graphical model implementation. We discuss in particular the roles of three major types of inhibitory neurons (small fast-spiking basket cells, large layer 2\/3 basket cells, and double-bouquet neurons), subpopulations of strongly interconnected neurons with their unique connectivity patterns in different cortical layers, and the possible role of minicolumns in the realization of the population-based maximum operation.<\/jats:p>","DOI":"10.1162\/neco.2009.05-08-783","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T21:39:40Z","timestamp":1250545180000},"page":"3010-3056","source":"Crossref","is-referenced-by-count":34,"title":["Cortical Circuitry Implementing Graphical Models"],"prefix":"10.1162","volume":"21","author":[{"given":"Shai","family":"Litvak","sequence":"first","affiliation":[{"name":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, 71600"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shimon","family":"Ullman","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, 71600"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300016827"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1038\/81453"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1038\/nature03010"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1109\/18.825794"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2037719100"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1002\/cne.10100"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.22-19-08633.2002"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.5.1344"},{"issue":"2","key":"B9","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1111\/j.2517-6161.1974.tb00999.x","volume":"36","author":"Besag J.","year":"1974","journal-title":"Journal of the Royal Statistical Society"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.1400-04.2004"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1093\/brain\/awf110"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1038\/377059a0"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(90)90060-D"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.5.889"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1016\/0306-4522(90)90097-N"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.20.1.91"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.20.1.118"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.neuro.27.070203.144152"},{"key":"B19","volume-title":"Bayesian brain","author":"Doya K.","year":"2007"},{"key":"B20","volume-title":"Neural engineering: Computation, representation, and dynamics in neurobiological systems","author":"Eliasmith C.","year":"2003"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2005.98"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1038\/415429a"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/1.1.1"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026501619075"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2003.06.005"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024138413082"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1152\/jn.2002.88.3.1128"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511815706"},{"issue":"1","key":"B29","first-page":"9","volume":"15","author":"Ghahramani Z.","year":"2002","journal-title":"IJPRAI"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1126\/science.274.5284.109"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1126\/science.287.5451.273"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00551.2006"},{"key":"B33","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-4388(03)00075-8"},{"key":"B34","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.17-20-07606.1997"},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1162\/0899766041941943"},{"key":"B36","doi-asserted-by":"publisher","DOI":"10.1126\/science.7761831"},{"key":"B37","first-page":"448","volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition","author":"Hinton G. 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