Mirko & Marcus’ paper is out in PLoS Computational Biology!

If grid cells encode non-spatial cognitive variables, they should be able to represent spaces of dimension greater than two.

Can grid cells construct unambiguous representations of higher-dimensional inputs without recurrent rewiring to form higher-dimensional grid responses, a cell-inefficient and inflexible mechanism?

We show how they could do so by combining low-dimensional random projections with “classical” two-dimensional hexagonal grid cell responses.

Without reconfiguration of the recurrent circuit, the same network 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.

This model achieves high efficiency and flexibility by combining two powerful concepts, modularity and mixed selectivity, in what we call “mixed modular coding”.