Efficient and flexible representation of higher-dimensional cognitive variables with grid cells
(a) Firing fields and their hexagonal arrangement shown for two simulated grid cells from two modules of different scale. (b) Schematic picture of the origin of periodic firing fields. Left: a schematic environment (black line) with cell responses (green, blue) of two grid cells from two modules of different scale. Right: schematic picture of two grid modules depicted as 1-dimensional circular continuous attractors. The colored triangles symbolize recording devices whose responses are shown on the left. A positional change (small arrow on left-hand side) corresponds to a change in phase (small arrows on right-hand side) in each module. Both phase-changes are related by a fixed scalar factor resulting in different spatial periodicity. (c) Schematic picture of the coding space (gray box) spanned by multiple, here 2, grid modules (blue and green). The modulo-arithmetic nature of the grid code enables an extraordinarily huge coding range by tightly “packing/folding” an environment (black line) into code space (gray). The fixed ratio of module scales results in a linear embedding with fixed “slope”.