  Many recent models study the downstream projection from grid cells to place
cells, while recent data has pointed out the importance of the feedback
projection. We thus asked how grid cells are affected by the nature of the
input from the place cells. We propose a two-layered neural network with
feedforward weights connecting place-like input cells to grid cell outputs.
Place-to-grid weights were learned via a generalized Hebbian rule. The
architecture of this network highly resembles neural networks used to perform
Principal Component Analysis (PCA). Our results indicate that if the components
of the feedforward neural network were non-negative, the output converged to a
hexagonal lattice. Without the non-negativity constraint the output converged
to a square lattice. Consistent with experiments, grid alignment to walls was
~7{\deg} and grid spacing ratio between consecutive modules was ~1.4. Our
results express a possible linkage between place-cell to grid-cell interactions
and PCA, suggesting that grid cells represent a process of constrained
dimensionality reduction that can be viewed also as a process of variance
maximization of the information from place-cells.
