Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks

TL;DR

This paper presents an analytically solvable model for two-dimensional continuous attractor neural networks, describing how they track stimuli and analyzing their dynamics using quantum harmonic oscillator basis functions.

Contribution

It introduces a novel analytical approach to model and analyze the dynamics of 2D CANNs, including distortion modes and reaction times.

Findings

Analytical solutions match simulation results.

Gaussian bumps effectively model neural responses.

Reaction times depend on stimulus changes.

Abstract

We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.