{"id":1822,"date":"2019-04-14T16:15:22","date_gmt":"2019-04-14T06:15:22","guid":{"rendered":"https:\/\/www.cognav.net\/?p=1822"},"modified":"2019-04-14T16:15:22","modified_gmt":"2019-04-14T06:15:22","slug":"how-grid-cells-generate-unambiguous-and-high-capacity-representations-of-variables-in-much-higher-dimensional-space","status":"publish","type":"post","link":"https:\/\/braininspirednavigation.com\/?p=1822","title":{"rendered":"How grid cells generate unambiguous and high-capacity representations of variables in much higher-dimensional space?"},"content":{"rendered":"<p>Klukas, Mirko, Marcus Lewis, and Ila Fiete. &#8220;<a href=\"https:\/\/www.biorxiv.org\/content\/10.1101\/578641v1.abstract\"><strong>Flexible representation and memory of higher-dimensional cognitive variables with grid cells<\/strong><\/a>.&#8221; bioRxiv (2019): 578641.<\/p>\n<p>The following content is from\u00a0Klukas 2019.<\/p>\n<p style=\"text-align: justify;\">Grid cell representations are simultaneously flexible and powerful yet rigid and constrained: On one hand, they can encode spatial or a variety of non-spatial cognitive variables (Constantinescu et al., 2016; Killian et al., 2012), with remarkable capacity, integration, and error correction properties (Fiete et al., 2008; Sreenivasan and Fiete, 2011; Mathis et al., 2012). On the other, states within each grid module are confined to a fixed two-dimensional (2D) set across time, environment, encoded variable (Yoon et al., 2013, 2016), behavioral states including sleep (Gardner et al., 2017; Trettel et al., 2017), with the inherent low-dimensionality etched directly into the physical topography of the circuit (Heys et al., 2014; Gu et al., 2018). <span style=\"color: red;\"><strong>The restriction to 2D states seemingly imposes a severe limit on the representation of general cognitive variables of dimension greater than two by grid cells<\/strong><\/span>.<\/p>\n<p style=\"text-align: justify;\">Klukas et al. 2019 show that <span style=\"color: red;\"><strong>a set of grid cell modules, each with only 2D responses, can generate unambiguous and high-capacity representations of variables in much higher-dimensional spaces<\/strong><\/span>. Specifically, M grid modules can represent variables of arbitrary dimension up to 2M, with a capacity exponential in M. The idea generalizes our understanding of <span style=\"color: red;\"><strong>the 2D grid code as capable of flexible reconfiguration to generate unique high-capacity metric codes and memory states for representation and algebra in higher-dimensional vector spaces, without costly higher-dimensional grid-like responses in individual cells<\/strong><\/span>.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2019\/04\/041419_0520_Howgridcell1.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: center;\">Fig. 4 Solution to the double ambiguity of grid cell representation: a three-dimensional example<\/p>\n<p style=\"text-align: center;\">Fig from Klukas et al. 2019.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2019\/04\/041419_0520_Howgridcell2.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: center;\">Figure 6: Predictions about grid cell firing and cell-cell relationships in higher dimensions.<\/p>\n<p style=\"text-align: center;\">Fig from Klukas et al. 2019.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">For further info, please read the paper Klukas et al. 2019.<\/p>\n<p style=\"text-align: justify;\">Klukas, Mirko, Marcus Lewis, and Ila Fiete. &#8220;<a href=\"https:\/\/www.biorxiv.org\/content\/10.1101\/578641v1.abstract\"><strong>Flexible representation and memory of higher-dimensional cognitive variables with grid cells<\/strong><\/a>.&#8221; bioRxiv (2019): 578641.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Klukas, Mirko, Marcus Lewis, and Ila Fiete. &#8220;Flexible representation and memory of higher-dimensional cognitive variables with grid cells.&#8221; bioRxiv (2019): 578641. The following content is from\u00a0Klukas 2019. Grid cell representations are simultaneously flexible and powerful yet rigid and constrained: On one hand, they can encode spatial or a variety of non-spatial cognitive variables (Constantinescu et [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[390,370,389,96,346,419],"tags":[103,458],"_links":{"self":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1822"}],"collection":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1822"}],"version-history":[{"count":2,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1822\/revisions"}],"predecessor-version":[{"id":1838,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1822\/revisions\/1838"}],"wp:attachment":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}