Non-equilibrium statistical mechanics of continuous attractors

TL;DR

This paper investigates the limits of how quickly continuous attractor neural networks can update their internal representations in response to external signals, with implications for understanding neural encoding of spatial and directional information.

Contribution

It introduces a theoretical framework for understanding the non-equilibrium dynamics of continuous attractors and derives a velocity-dependent memory capacity in neural networks.

Findings

Identifies fundamental limits on updating rates of internal representations.

Derives a velocity-dependent non-equilibrium memory capacity.

Provides insights into neural encoding of spatial and head direction signals.

Abstract

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent non-equilibrium memory capacity in neural networks.