Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

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Abstract

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 single-layer 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). Both numerical results and analytic considerations 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 spacing ratio between the first two consecutive modules was ~1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

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Yedidyah Dordek

Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel

Competing interests
The authors declare that no competing interests exist.
Daniel Soudry

Department of Statistics, Columbia University, New York, United States

Competing interests
The authors declare that no competing interests exist.
Ron Meir

Faculty of Electrical Engineering, Technion - Israel Institute Of technology, Haifa, Israel

Competing interests
The authors declare that no competing interests exist.
Dori Derdikman

Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel

For correspondence
derdik@technion.ac.il

Competing interests
The authors declare that no competing interests exist.

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