Rectangular grid-like spatial tuning emerges qualitatively in a vanilla RNN

Cueva & Wei train a vanilla tanh RNN end-to-end on 2D path integration (estimating position from velocity in square and triangular arenas), with no architectural imposition of periodicity [cueva-wei-2018-grid-like-representations] Grid-like periodic spatial tuning, plus border and band cells, emerges in individual unit activity, a genuinely discovered structure [cueva-wei-2018-grid-like-representations] The identification is qualitative and visual (inspection of firing-rate maps): the paper computes no gridness score or spatial autocorrelogram [cueva-wei-2018-grid-like-representations] Grid geometry conforms to the enclosure shape: a square arena gives rectangular (not hexagonal) grids, while hexagonal/triangular arenas give closer-to-triangular grids [cueva-wei-2018-grid-like-representations]