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Properties of an invariant set of weights of perceptrons

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5 Author(s)

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.

Published in:

Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence). IEEE International Joint Conference on

Date of Conference:

1-8 June 2008