On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors

Norikazu Takahashi; Yasuhiro Minetoma

doi:10.1109/IJCNN.2008.4633836

On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors

Norikazu Takahashi, Yasuhiro Minetoma

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

Original language	English
Title of host publication	2008 International Joint Conference on Neural Networks, IJCNN 2008
Pages	484-489
Number of pages	6
DOIs	https://doi.org/10.1109/IJCNN.2008.4633836
Publication status	Published - Nov 24 2008
Externally published	Yes
Event	2008 International Joint Conference on Neural Networks, IJCNN 2008 - Hong Kong, China Duration: Jun 1 2008 → Jun 8 2008

Publication series

Name	Proceedings of the International Joint Conference on Neural Networks

Other

Other	2008 International Joint Conference on Neural Networks, IJCNN 2008
Country/Territory	China
City	Hong Kong
Period	6/1/08 → 6/8/08

ASJC Scopus subject areas

Software
Artificial Intelligence

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10.1109/IJCNN.2008.4633836

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Takahashi, N., & Minetoma, Y. (2008). On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors. In 2008 International Joint Conference on Neural Networks, IJCNN 2008 (pp. 484-489). Article 4633836 (Proceedings of the International Joint Conference on Neural Networks). https://doi.org/10.1109/IJCNN.2008.4633836

On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors. / Takahashi, Norikazu; Minetoma, Yasuhiro.
2008 International Joint Conference on Neural Networks, IJCNN 2008. 2008. p. 484-489 4633836 (Proceedings of the International Joint Conference on Neural Networks).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Takahashi, N & Minetoma, Y 2008, On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors. in 2008 International Joint Conference on Neural Networks, IJCNN 2008., 4633836, Proceedings of the International Joint Conference on Neural Networks, pp. 484-489, 2008 International Joint Conference on Neural Networks, IJCNN 2008, Hong Kong, China, 6/1/08. https://doi.org/10.1109/IJCNN.2008.4633836

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AB - Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

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On asymptotic behavior of state trajectories of piecewise-linear recurrent neural networks generating periodic sequence of binary vectors

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