Velocity coupling of grid cell modules enables stable embedding of a low dimensional variable in a high dimensional neural attractor

Grid cells in the medial entorhinal cortex (MEC) encode position using a distributed representation across multiple neural populations (modules), each possessinga distinct spatial scale. The modular structure of the representation confers the grid cell neural code with large capacity. Yet, the modularity poses significant challenges for the neural circuitry that maintains the representation, and updates it based on self motion. Small incompatible drifts in different modules, driven by noise, can rapidly lead to large, abrupt shifts in the represented position, resulting in catastrophic readout errors. Here we propose a theoretical model of coupled modules. The coupling suppresses incompatible drifts, allowing for a stable embedding of a two dimensional variable (position) in a higher dimensional neural attractor, while preserving the large capacity. We propose that coupling of this type may be implemented by recurrent synaptic connectivity within the MEC with a relatively simple and biologically plausible structure.