High-resolution spatial memory requires grid-cell-like neural codes

TL;DR

This paper introduces a novel neural coding scheme inspired by grid cells that allows continuous attractor networks to maintain high-resolution spatial memory with robustness to imperfections, overcoming traditional stability-resolution trade-offs.

Contribution

The work proposes a new grid-cell-like coding approach for continuous attractor networks, enabling both high stability and high resolution in spatial memory representation.

Findings

Grid-cell-like codes enable stable, high-resolution spatial memory.

The model generalizes to arbitrary nonlinear manifolds.

Simulations confirm theoretical advantages of the proposed coding scheme.

Abstract

Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory mechanism is very sensitive to even small imperfections, such as noise or heterogeneity, which are both common in biological systems. Previous work has shown that discretising the continuum into a finite set of discrete attractor states provides robustness to these imperfections, but necessarily reduces the resolution of the represented variable, creating a dilemma between stability and resolution. We show that this stability-resolution dilemma is most severe for CANs using unimodal bump-like codes, as in traditional models. To overcome this, we investigate sparse binary distributed codes based on random feature embeddings, in which neurons have spatially-periodic receptive fields. We demonstrate theoretically and with simulations that such grid-cell-like codes enable CANs to achieve both high stability and high resolution simultaneously. The model extends to embedding arbitrary nonlinear manifolds into a CAN, such as spheres or tori, and generalises linear path integration to integration along freely-programmable on-manifold vector fields. Together, this work provides a theory of how the brain could robustly represent continuous variables with high resolution and perform flexible computations over task-relevant manifolds.