Representations of continuous attractors of recurrent neural networks

Authors:
Jiali Yu;Zhang Yi;Lei Zhang
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China;Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu, China;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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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.