Self-Supervised Learning of Representations for Space Generates Multi-Modular Grid Cells

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, synthesis of multi-modular grid cells in deep recurrent neural networks remains absent. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: dynamical systems, coding theory, function optimization and supervised deep learning.