PT  - JOURNAL ARTICLE
AU  - Klukas, Mirko
AU  - Lewis, Marcus
AU  - Fiete, Ila
TI  - Flexible representation of higher-dimensional cognitive variables with grid cells
AID  - 10.1101/578641
DP  - 2019 Jan 01
TA  - bioRxiv
PG  - 578641
4099  - http://biorxiv.org/content/early/2019/08/28/578641.short
4100  - http://biorxiv.org/content/early/2019/08/28/578641.full
AB  - We shed light on the theoretical capabilities of entorhinal grid cells to encode variables of dimension greater than two. Our model constructs representations of high-dimensional inputs through a combination of low-dimensional random projections and “classical” low-dimensional hexagonal grid cell responses. Without reconfiguration of the recurrent circuit, the same system can flexibly encode multiple variables of different dimensions while maximizing the coding range (per dimension) by automatically trading-off dimension with an exponentially large coding range. In contrast to previously proposed schemes, the model does not require the formation of higher-dimensional grid responses, a cell-inefficient and rigid mechanism. The firing fields observed in flying bats or climbing rats can be generated by neurons that combine activity from multiple grid modules, each representing higher-dimensional spaces according to our model. The idea expands our understanding of grid cells, suggesting that they could implement a general circuit that generates on-demand coding and memory states for variables in high-dimensional vector spaces.