A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements

Masaya OHTA; Yoichiro ANZAI; Shojiro YONEDA; Akio OGIHARA

A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements

Masaya OHTA, Yoichiro ANZAI, Shojiro YONEDA, Akio OGIHARA

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This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.3 pp.284-291

Publication Date: 1993/03/25

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Type of Manuscript: Special Section PAPER (Special Section on the 5th Karuizawa Workshop on Circuits and Systems)

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Masaya OHTA, Yoichiro ANZAI, Shojiro YONEDA, Akio OGIHARA, "A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 3, pp. 284-291, March 1993, doi: .
Abstract: This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e76-a_3_284/_p

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@ARTICLE{e76-a_3_284,
author={Masaya OHTA, Yoichiro ANZAI, Shojiro YONEDA, Akio OGIHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements},
year={1993},
volume={E76-A},
number={3},
pages={284-291},
abstract={This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - A Theoretical Analysis of Neural Networks with Nonzero Diagonal Elements
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 284
EP - 291
AU - Masaya OHTA
AU - Yoichiro ANZAI
AU - Shojiro YONEDA
AU - Akio OGIHARA
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1993
AB - This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.
ER -