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

Yedidyah Dordek,Ron Meir,Daniel Soudry,Dori Derdikman

doi:10.7554/elife.10094

Abstract

Many recent models study the downstream projection from grid cells to place cells, while recent data have 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 are 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 are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is -1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

Highlights

The system of spatial navigation in the brain has recently received much attention (Burgess, 2014; Morris, 2015; Eichenbaum, 2015)
A notable exception to this class of models was suggested in a previous paper by Kropff and Treves (2008); and in a sequel to that paper (Si and Treves, 2013), in which they demonstrated the emergence of grid cells from place cell inputs without using the rat’s velocity as an input signal
We initially considered the output of a single-layer neural network and of the Principal Component Analysis (PCA) algorithm in response to the same inputs

Summary

Introduction

The system of spatial navigation in the brain has recently received much attention (Burgess, 2014; Morris, 2015; Eichenbaum, 2015). The details of these mechanisms differ, they mostly share in common the assumption that the animal’s velocity is the main input to the system (Derdikman and Knierim, 2014; Zilli, 2012; Giocomo et al, 2011), such that positional information is generated by the integration of this input in time. This process is termed ’path integration’ (PI) (Mittelstaedt and Mittelstaedt, 1980). A notable exception to this class of models was suggested in a previous paper by Kropff and Treves (2008); and in a sequel to that paper (Si and Treves, 2013), in which they demonstrated the emergence of grid cells from place cell inputs without using the rat’s velocity as an input signal

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Conclusion