A unified theory for the computational and mechanistic origins of grid cells

The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might emerge in a generic manner from neural circuits, and what their computational significance might be. Here, we forge a link between the problem of path integration and the existence of hexagonal grids, by demonstrating that such grids arise in neural networks trained to path integrate under simple biologically plausible constraints. Moreover, we develop a unifying theory for why hexagonal grids are ubiquitous in path-integrator circuits. Such trained networks also yield powerful mechanistic hypotheses, exhibiting realistic levels of biological variability not captured by hand-designed models. We furthermore develop methods to analyze the connectome and activity maps of our networks to elucidate fundamental mechanisms underlying path integration. These methods provide a road map to go from connectomic and physiological measurements to conceptual understanding in a manner that could generalize to other settings.