title: Representations of continuous attractors of recurrent neural networks.
abstract: A continuous attractor of a recurrent neural network (RNN) is a set of connected stable equilibrium points. Continuous attractors have been used to describe the encoding of continuous stimuli in neural networks. Dynamic behaviors of continuous attractors of RNNs exhibit interesting properties. This brief desires to derive explicit representations of continuous attractors of RNNs. Representations of continuous attractors of linear RNNs as well as linear-threshold (LT) RNNs are obtained under some conditions. These representations could be looked at as solutions of continuous attractors of the networks. Such results provide clear and complete descriptions to the continuous attractors.
authors.affiliation: School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China. yujiali@uestc.edu.cn
authors.forename: Jiali
authors.initials: J
authors.lastname: Yu
authors.forename: Zhang
authors.initials: Z
authors.lastname: Yi
authors.forename: Lei
authors.initials: L
authors.lastname: Zhang