Are Grid Cells Hexagonal for Performance or by Convenience?

TL;DR

The 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).

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).

Figures (12)

• Figure 1: Examples of recalled images using a noisy input for all three datasets. The cosine similarity between the recalled image and the original is written below the recalled image.
• Figure 2: Examples of the different path types used: regular line, Brownian motion, and Lévy flight.
• Figure 3: Average Cosine Similarity Scores vs % of Theoretical Maximal Memory Capacity Filled for Different Image Datasets: MNIST, Fashion MNIST, and CIFAR.
• Figure 4: Cosine Similarity Recall Scores vs Number of grid cells, $N_g$, and hippocampal place cells, $N_h$.
• Figure 5: MNIST: Cosine Similarity Recall Scores vs Path Type and Path Length