{"id":2128,"date":"2019-12-12T13:49:43","date_gmt":"2019-12-12T03:49:43","guid":{"rendered":"https:\/\/www.cognav.net\/?p=2128"},"modified":"2019-12-12T13:49:56","modified_gmt":"2019-12-12T03:49:56","slug":"how-the-grid-cells-perform-path-integral-path-planning-and-error-correction","status":"publish","type":"post","link":"https:\/\/braininspirednavigation.com\/?p=2128","title":{"rendered":"How the grid cells perform path integral, path planning and error correction?"},"content":{"rendered":"<p style=\"text-align: justify;\">Gao, Ruiqi &amp; Xie, Jianwen &amp; Zhu, Song &amp; Wu, Yingnian.\u00a0\u00a0<a href=\"https:\/\/www.researchgate.net\/publication\/328280545_Learning_Grid_Cells_as_Vector_Representation_of_Self-Position_Coupled_with_Matrix_Representation_of_Self-Motion\">Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion<\/a>. ICLR 2019<\/p>\n<p style=\"text-align: justify;\">Abstract<\/p>\n<p style=\"text-align: justify;\">&#8220;<strong><span style=\"color: #ff0000;\">This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector<\/span><\/strong>. Each component of the vector is a unit or a cell. The model consists of the following three sub-models. (1) <strong><span style=\"color: #ff0000;\">Vector-matrix multiplication<\/span><\/strong>. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., the vector of the next position is obtained by multiplying the matrix of the motion to the vector of the current position. (2) <strong><span style=\"color: #ff0000;\">Magnified local isometry<\/span><\/strong>. The angle between two nearby vectors equals the Euclidean distance between the two corresponding positions multiplied by a magnifying factor. (3) <strong><span style=\"color: #ff0000;\">Global adjacency kernel.<\/span><\/strong> The inner product between two vectors measures the adjacency between the two corresponding positions, which is defined by a kernel function of the Euclidean distance between the two positions. <strong><span style=\"color: #ff0000;\">Our representational model has explicit algebra and geometry<\/span><\/strong>. It can learn hexagon patterns of grid cells, and <strong><span style=\"color: #ff0000;\">it is capable of error correction, path integral and path planning<\/span><\/strong>.&#8221;<\/p>\n<p style=\"text-align: justify;\">Gao, Ruiqi &amp; Xie, Jianwen &amp; Zhu, Song &amp; Wu, Yingnian. (2018). <a href=\"https:\/\/www.researchgate.net\/publication\/328280545_Learning_Grid_Cells_as_Vector_Representation_of_Self-Position_Coupled_with_Matrix_Representation_of_Self-Motion\">Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion<\/a>. ICLR 2019<\/p>\n<p style=\"text-align: justify;\">GridCell-3D Code:\u00a0<a href=\"https:\/\/github.com\/jianwen-xie\/GridCell-3D\">https:\/\/github.com\/jianwen-xie\/GridCell-3D<\/a>\u00a0<\/p>\n<p style=\"text-align: justify;\">GridCell Code:\u00a0<a href=\"https:\/\/github.com\/ruiqigao\/GridCell\">https:\/\/github.com\/ruiqigao\/GridCell<\/a><\/p>\n<p style=\"text-align: justify;\">Project:\u00a0<a href=\"http:\/\/www.stat.ucla.edu\/~ruiqigao\/gridcell\/main.html\">http:\/\/www.stat.ucla.edu\/~ruiqigao\/gridcell\/main.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gao, Ruiqi &amp; Xie, Jianwen &amp; Zhu, Song &amp; Wu, Yingnian.\u00a0\u00a0Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion. ICLR 2019 Abstract &#8220;This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[390,389,96,376,346],"tags":[347,98,618,619],"_links":{"self":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/2128"}],"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=2128"}],"version-history":[{"count":2,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/2128\/revisions"}],"predecessor-version":[{"id":2130,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/2128\/revisions\/2130"}],"wp:attachment":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}