Flexible representation of higher-dimensional cognitive variables with grid cells

Abstract

Grid cell representations are simultaneously flexible and powerful yet rigid and constrained:

Fragmented Spatial Maps from Surprisal: State Abstraction and Efficient Planning

“…We assume that internally locations are represented by a population of idealized grid cells of mulitple scales. For ease of computation, we interpret this multi-module grid code as a high capcity code for an unfolded 2-dimensional space [11]; cf. Fig.…”

“…Our model of online fragmentation of a continuous stream of experience enables the representation of a very general class of maps -including in spatial and non-spatial cognitive domains -in a way that exceeds the capabilities of a "pure" grid code. Grid cells generate Euclidean representations of Euclidean spaces [11]. Fragmented maps can each be viewed as separate local Euclidean "charts", mapped out by a multi-modular grid code, that are then associated to each other through transitions learned in the hippocampus according to the global layout of the charts.…”

“…Thus, from a general perspective, map fragmentation and remapping (reanchoring) on cognitive representations can be viewed as faciliating the step from representing flat Euclidean space to representing richer manifolds. In combination with grid cells' ability to represent high-dimensional variables [11], such a coding scheme becomes highly expressive.…”

“…Instead, we propose that the neural codes seen within submaps retain their native structure across spaces, in the form of a pre-formed and stable recurrent sca↵old for memory through grid cells. Even though grid cell representations in each module are 2-dimensional, theoretically the set of modules an represent even high-dimensional continuous spaces [11], while potential non-Euclidean aspects of cognitive varaibles can be captured by the between-submap transitions. This structuring of memory into continuous parts with preexisting sca↵olds [59][60][61][62][63] together with occasional transitions between these continuous chunks simultaneously provides rapid learning and flexibility.…”

“…1a. The advantage of such velocity integration-based Euclidean representations is that they provide a consistent encoding of seen and unseen locations and independent of paths taken to get there, making it possible to compute novel shortcut paths between locations [7][8][9][10][11].…”