Dynamics of Neural Networks with Continuous Attractors

TL;DR

This paper analyzes the dynamics of continuous attractor neural networks, focusing on their stability, tracking capabilities, and response to stimuli, with a perturbative approach to quantify shape distortions and performance limits.

Contribution

It introduces a perturbative method to study CANN dynamics, revealing how neutral stability affects tracking performance and shape distortions during stimulus movement.

Findings

Maximum trackable stimulus speed quantified.

Reaction time to stimulus change analyzed.

Shape distortions impact tracking accuracy.

Abstract

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.