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Grid cells in the entorhinal cortex, together with head direction, place,speed and border cells, are major contributors to the organization of spatialrepresentations in the brain. In this work we introduce a novel theoretical andalgorithmic framework able to explain the emergence of hexagonal grid-likeresponse patterns from head direction cells' responses. We show that thispattern is a result of minimal variance encoding of neurons. The novelty liesinto the formulation of the encoding problem through the modern Frame Theorylanguage, specifically that of equiangular Frames, providing new insights aboutthe optimality of hexagonal grid receptive fields. The model proposed overcomessome crucial limitations of the current attractor and oscillatory models. It isbased on the well-accepted and tested hypothesis of Hebbian learning, providinga simplified cortical-based framework that does not require the presence oftheta velocity-driven oscillations (oscillatory model) or translationalsymmetries in the synaptic connections (attractor model). We moreoverdemonstrate that the proposed encoding mechanism naturally explains axisalignment of neighbor grid cells and maps shifts, rotations and scaling of thestimuli onto the shape of grid cells' receptive fields, giving astraightforward explanation of the experimental evidence of grid cellsremapping under transformations of environmental cues.

A computational model for grid maps in neural populations