Dynamics of Adaptive Continuous Attractor Neural Networks

TL;DR

This paper explores the complex dynamics of adaptive continuous attractor neural networks (A-CANNs), providing a unified mathematical framework to understand their behaviors and implications for brain function.

Contribution

It offers a comprehensive analysis of A-CANN dynamics and introduces a unified mathematical approach to interpret their diverse behaviors.

Findings

A-CANNs exhibit rich and diverse dynamical behaviors.

A unified mathematical framework explains these behaviors.

Implications for understanding brain functions are discussed.

Abstract

Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information robustly, but it also incurs the difficulty of rapid update of network states, which can impair information update and search in the brain. To overcome this difficulty, a solution is to include adaptation in the attractor network dynamics, whereby the adaptation serves as a slow negative feedback mechanism to destabilize which are otherwise permanently stable states. In such a way, the neural system can, on one hand, represent information reliably using attractor states, and on the other hand, perform computations wherever rapid state updating is involved. Previous studies have shown that continuous attractor neural networks with adaptation (A-CANNs) exhibits rich dynamical behaviors accounting for various brain functions. In this paper, we present a comprehensive view of the rich diverse dynamics of A-CANNs. Moreover, we provide a unified mathematical framework to understand these different dynamical behaviors, and briefly discuss about their biological implications.