Properties of an invariant set of weights of perceptrons

Ho, Charlotte Yuk-Fan and Ling, Bingo Wing-Kuen and Nasir, Muhammad Habib Ullah and Lam, Hak-Keung and Iu, Herbert H C (2008) Properties of an invariant set of weights of perceptrons. In: International Joint Conference on Neural Networks 2008, 1 - 8 June 2008, Hong Kong.

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Official URL: http://dx.doi.org/10.1109/IJCNN.2008.4634015

Abstract

In this paper, the dynamics of weights of perceptrons are investigated based on the perceptron training algorithm. In particular, the condition that the system map is not injective is derived. Based on the derived condition, an invariant set that results to a bijective invariant map is characterized. Also, it is shown that some weights outside the invariant set will be moved to the invariant set. Hence, the invariant set is attracting. Computer numerical simulation results on various perceptrons with exhibiting various behaviors, such as fixed point behaviors, limit cycle behaviors and chaotic behaviors, are illustrated.

Item Type:Conference or Workshop Item (Paper)
Additional Information:In this paper, the dynamics of weights of perceptrons are investigated based on the perceptron training algorithm. In particular, the condition that the system map is not injective is derived. Based on the derived condition, an invariant set that results to a bijective invariant map is characterized. Also, it is shown that some weights outside the invariant set will be moved to the invariant set. Hence, the invariant set is attracting. Computer numerical simulation results on various perceptrons with exhibiting various behaviors, such as fixed point behaviors, limit cycle behaviors and chaotic behaviors, are illustrated.
Keywords:weights of perceptrons, various behaviours, Perceptron training algorithm
Subjects:H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:2725
Deposited By: Rosaline Smith
Deposited On:25 Jun 2010 09:02
Last Modified:13 Mar 2013 08:40

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