Extracting grid characteristics from spatially distributed place cell inputs using non-negative PCA

TL;DR

This paper models how grid cells develop their characteristic patterns from place cell inputs using a neural network resembling PCA, revealing that non-negative constraints produce hexagonal grids and linking grid formation to dimensionality reduction.

Contribution

It introduces a neural network model that links place-to-grid cell interactions with PCA, showing how non-negative constraints lead to hexagonal grid patterns.

Findings

Non-negative PCA leads to hexagonal grid patterns.

Without non-negativity, grid patterns are square.

Grid alignment and spacing ratios match experimental data.

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 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.