### Abstract

S. A. Kauffman explored the law of self-organization in random Boolean networks, and K. Inagaki also did it in neural networks partially. The aim of this paper is to show that probabilistic neural networks (PNNs) hold the order, even though the weights, the thresholds, and the connections between neurons are determined randomly; where PNNs are recurrent networks and controlled by a probabilistic transition rule based on a Boltzmann machine. In addition, the deterministic transient neural networks (DNNs) which are the special networks of PNNs are studied extensively. From simulations, it is shown that in DNNs the dynamics follow the square-root law and there is another new critical point as for the distribution of the thresholds. In addition, it is shown that in PNNs the averages of the Hamming distance between the attractors of DNN and PNN stay around a certain value depending on the thresholds and the gradient of the Sigmoidal function. These results can be explained by the sensitivity to the initial conditions of DNNs.

Original language | English |
---|---|

Pages (from-to) | 2533-2538 |

Number of pages | 6 |

Journal | Proceedings of the IEEE International Conference on Systems, Man and Cybernetics |

Volume | 4 |

Publication status | Published - Dec 1 2000 |

Event | 2000 IEEE International Conference on Systems, Man and Cybernetics - Nashville, TN, USA Duration: Oct 8 2000 → Oct 11 2000 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Hardware and Architecture

### Cite this

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics*,

*4*, 2533-2538.

**Self-organization in probabilistic neural networks.** / Shiraishi, Yuhki; Hirasawa, Kotaro; Hu, Jinglu; Murata, Junichi.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics*, vol. 4, pp. 2533-2538.

}

TY - JOUR

T1 - Self-organization in probabilistic neural networks

AU - Shiraishi, Yuhki

AU - Hirasawa, Kotaro

AU - Hu, Jinglu

AU - Murata, Junichi

PY - 2000/12/1

Y1 - 2000/12/1

N2 - S. A. Kauffman explored the law of self-organization in random Boolean networks, and K. Inagaki also did it in neural networks partially. The aim of this paper is to show that probabilistic neural networks (PNNs) hold the order, even though the weights, the thresholds, and the connections between neurons are determined randomly; where PNNs are recurrent networks and controlled by a probabilistic transition rule based on a Boltzmann machine. In addition, the deterministic transient neural networks (DNNs) which are the special networks of PNNs are studied extensively. From simulations, it is shown that in DNNs the dynamics follow the square-root law and there is another new critical point as for the distribution of the thresholds. In addition, it is shown that in PNNs the averages of the Hamming distance between the attractors of DNN and PNN stay around a certain value depending on the thresholds and the gradient of the Sigmoidal function. These results can be explained by the sensitivity to the initial conditions of DNNs.

AB - S. A. Kauffman explored the law of self-organization in random Boolean networks, and K. Inagaki also did it in neural networks partially. The aim of this paper is to show that probabilistic neural networks (PNNs) hold the order, even though the weights, the thresholds, and the connections between neurons are determined randomly; where PNNs are recurrent networks and controlled by a probabilistic transition rule based on a Boltzmann machine. In addition, the deterministic transient neural networks (DNNs) which are the special networks of PNNs are studied extensively. From simulations, it is shown that in DNNs the dynamics follow the square-root law and there is another new critical point as for the distribution of the thresholds. In addition, it is shown that in PNNs the averages of the Hamming distance between the attractors of DNN and PNN stay around a certain value depending on the thresholds and the gradient of the Sigmoidal function. These results can be explained by the sensitivity to the initial conditions of DNNs.

UR - http://www.scopus.com/inward/record.url?scp=0034506641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034506641&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0034506641

VL - 4

SP - 2533

EP - 2538

JO - Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

JF - Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

SN - 0884-3627

ER -