Analysis of continuous attractors for 2-D linear threshold neural networks

Authors:
Lan Zou;Huajin Tang;Kay Chen Tan;Weinian Zhang
Affiliations:
Yangtze Center of Mathematics and the Department of Mathematics, Sichuan University, Chengdu, China;Institute for Infocomm Research, Agency for Science, Technology and Research, Singapore, Singapore;Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore;Yangtze Center of Mathematics and the Department of Mathematics, Sichuan University, Chengdu, China
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

This brief investigates continuous attractors of the well-developed model in visual cortex, i.e., the linear threshold (LT) neural networks, based on a parameterized 2-D model. On the basis of existing results on nondegenerate equilibria in mathematics, we further discuss degenerate equilibria for such networks and present properties and distributions of the equilibria, which enables us to draw the coexistence conditions of nondegenerate and degenerate equilibria (e.g., singular lines). Our theoretical results provide a useful framework for precise tuning on the network parameters, e.g., the feedbacks and visual inputs. Simulations are also presented to illustrate the theoretical findings.