טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentYedidyah Dordek
SubjectFrom Place-Cells to Grid-cells: A Trip between
Dimensions
DepartmentDepartment of Electrical Engineering
Supervisors Full Professor Meir Ron
Professor Derdikman Dori
Full Thesis textFull thesis text - English Version


Abstract

The precise interaction between different spatially-dependent nerve cells in the hippocampal formation in the brain is under debate. These cells are active when the mammal receives location oriented input with respect to some spatial context.  Among those cells, two have attracted much attention in recent years; the "place-cells" and the "grid-cells". Place-cells respond to localized regions in space and have only a single (or very few) firing fields in a given environment. Grid-cells, however, fire in multiple locations in the environment in a regular pattern that forms a hexagonal array. Being connected by bi-directional synapses, many models study the downstream projection from grid-cells to place-cells. However, 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 place-cells.

We propose a two-layered neural network with feedforward weights connecting place-like input cells to grid-cell outputs. The network was trained by moving a virtual agent randomly in a two-dimensional space. 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 weights of the feed-forward neural network were enforced to be non-negative, as expected from an excitatory projection, the final output converged to a hexagonal lattice. However, without the non-negativity constraint we obtained mostly square-lattice results. The emergence of the specific hexagonal shape was investigated in terms of stability and maximum variance.

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 variance maximization of the information from place-cells.