An Efficient Coding Theory for a Dynamic Trajectory Predicts non-Uniform Allocation of Grid Cells to Modules in the Entorhinal Cortex

TL;DR

This paper presents a theory for efficient coding of spatial position by grid cells in the entorhinal cortex, predicting module size distributions and proposing a neural readout scheme aligned with experimental data.

Contribution

It introduces a novel efficient coding model that accounts for the organization and population sizes of grid cell modules based on animal motion statistics.

Findings

Module population sizes decrease sharply with grid spacing.

The proposed readout scheme matches Bayesian decoding accuracy.

Predictions align with experimental observations of grid cell organization.

Abstract

Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trends seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder of the spikes. This readout scheme requires persistence over varying timescales, ranging from ~1ms to ~1s, depending on the grid cell module. Our results suggest that the brain employs an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory coding.