Are Grid Cells Hexagonal for Performance or by Convenience?

TL;DR

This study compares hexagonal and square grid cells in spatial memory tasks, finding no significant performance difference, suggesting hexagonal grids are used more for biological convenience than for functional superiority.

Contribution

It provides the first direct comparison of hexagonal and square grid cells' performance in spatial memory tasks using a biologically inspired model.

Findings

Hexagonal and square grid cells show similar accuracy in memory recall.

Performance is robust across different noise levels and datasets.

Hexagonal grids may be favored for biological reasons rather than performance.

Abstract

This paper investigates whether the hexagonal structure of grid cells provides any performance benefits or if it merely represents a biologically convenient configuration. Utilizing the Vector-HaSH content addressable memory model as a model of the grid cell -- place cell network of the mammalian brain, we compare the performance of square and hexagonal grid cells in tasks of storing and retrieving spatial memories. Our experiments across different path types, path lengths and grid configurations, reveal that hexagonal grid cells perform similarly to square grid cells with respect to spatial representation and memory recall. Our results show comparable accuracy and robustness across different datasets and noise levels on images to recall. These findings suggest that the brain's use of hexagonal grids may be more a matter of biological convenience and ease of implementation rather than because they provide superior performance over square grid cells (which are easier to implement in silico).