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EXACT SYNTHESIS OF ASSOCIATIVE MEMORY CIRCUITS BY MEANS OF RECURSIVE NEURAL NETWORKS

Research Project

Project/Area Number 05452211
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field System engineering
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

NISHI Tetsuo  KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,PROFESSOR, 工学部, 教授 (40037908)

Co-Investigator(Kenkyū-buntansha) OOHAMA Yasusada  KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,RESEARCH ASSOCIATE, 工学部, 助手 (20243892)
KAWANE Yuji  KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,RESEARCH ASSOCIATE, 工学部, 助手 (30214662)
KOHDA Tohru  KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,PROFESSOR, 工学部, 教授 (20038102)
KOGA Tosiro  KURUME INSTITUTE OF TECHNOLOGY,PROFESSOR, 知能工学研究所, 教授 (00037706)
栖原 淑郎  九州大学, 工学部, 助手 (80187799)
Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1994: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1993: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsAssociative Memory / Neural Network / Storage Capacity / Recursive Neural Network / Stable Equilibrium / Limit Cycle
Research Abstract

The results obtained in the research term (1993-1994) are as follows :
1. We consider a neural network in which n neurons are arranged on a ring. We assume that each neuron is connected only with the preceding k (*n-1) neurons and the coefficients of connections are tapered, that is, the magnitude of coefficients decrease along with distance. This model is derived from the real biological knowledge and is a special kind of CNNs (Cellular Neural Network). We examined the number of equilibrium points of the above neural networks and proved that (1) the number is only one for k=1 or 2, three for k=3, and four for k=4.
2. We may conjecture that the number of equilibrium points are extremely few for tapered neural networks. We therefore examined another limiting case where k=n-1 and the magnitude of each coefficients is unity. We showed in this case that (1) there exist a network which can possess are at least 2^n/2 equilibrium points, and (2) there exists a network which can possess at least 2^n/4 stable equilibrium points. Thus we showed that the number of equilibrium points increases exponentially with k.
3. Concerning the stability of the CNN,we generalized the theorem recently given by Gilli. Gilli's theorem requires for a prescribed matrix A the condition that there exists a positive diagonal matrix D such that DA+A^TD is a symmetric matrix, while our theorem requires that GAMMA A+A^T GAMMA is a symmetric matrix where GAMMA is a positive definite matrix.
4. We gave the necessary and sufficient condition for a set of equilibrium points to be realizable by means of a neural network whose all diagonal elements have identical value and all nondiagonal elements are also identical.
5. In general equilibrium points correspond to solutions of a nonlinear resistive circuits. So we investigated about the number of solutions of these circuits and had many presentations as shown in REFERENCES below.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (45 results)

All Other

All Publications (45 results)

  • [Publications] T.Nishi: "Necessary and Sufficient Condition for the Basic Equation of Nonlinear Resistive Circuits Containing Ideal Diodes to Have a Unique Solution" IEICE Transaction. E76-A. 858-866 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Research Topics and Results on Nonlinear Circuits and Systems" IEICE Transaction. E76-A. 1077-1086 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Kawane: "An Analysis of Nonlinear Resistive Circuits Including Ideal Diodes by the Use of Scattering Matrix" KITE Journal. Vol.4. 45-51 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Kawane: "An Algorithm for Solving an Equation of Resistive Circuits Including Ideal Diodes as a Nonlinear Resistor" Proceedings of JTC-CSCC'93. Vol.1. 1-5 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahashi: "Realization of Certain Sets of Equilibrium Points by a Simple Neural Network" Proceedings of JTC-CSCC'93. Vol.1. 792-796 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Necessary and Sufficient Condition for Nonlinear Resistive Circuits Containing Ideal Diodes to have a Unique Solution" Proceedings of ECCTD'93. 1661-1666 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahashi: "Equilibrium Points of Mutually Coupled Symmetrical Neural Networks" Proceedings of ECCTD'93. 1059-1064 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Oohama: "An Evaluation of Statistical Properties of Pseudo-Random Numbers Generated by One-Dimensional Maps" Proceedings of NOLTA'93. 971-974 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T,Nishi: "On the Realization of Prescribed Sets of Equilibrium Points of One-Dimensional Neural Networks with Tapered Connecting Coefficients" Proceedings of NOLTA'93. 235-238 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahashi,T.Nishi: "Realization of Equilibrium Points by Means of Completely Symmetrical Nonlinear Circuits" 九州大学工学部紀要. Vol.54. 141-160 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahashi,T.Nishi: "On the Equilibrium Points of Hopfield-Type Neural Networks with the Cyclic Connection Matrix" Proceedings of NOLTSA'94. 21-24 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Necessary and Sufficient Condition for the Basic Equation of Nonlinear Resistive Circuits Containing Ideal Diodes to Have a Unique Solution" IEICE Transaction. E76-A. 858-866 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Research Topics and Results on Nonlinear Circuits and Systems" IEICE Transaction. E76-A. 1077-1086 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Kawane: "An Analysis of Nonlinear Resistive Circuits Including Ideal Diodes by the Use of Scattering Matrix" KITE Journal. Vol.4. 45-51 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Kawane: "An Algorithm for Solving an Equation of Resistive Circuits Including Ideal Diodes as a Nonlinear Resistor" Proceedings of JTC-CSCC'93. Vol.1. 1-5 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahashi: "Realization of Certain Sets of Equilibrium Plints by a Simple Neural Network" Proceedings of JTC-CSCC'93. Vol.1. 792-796 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Necessary and Sufficient Condition for Nonlinear Resistive Circuits Containing Ideal Diodes to have a Unique Solution" Proceedings of ECCTD'93. 1661-1666 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahasi: "Equilibrium Points of Mutually Coupled Symmetrical Neural Networks" Proceedings of ECCTD'93. 1059-1064 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Oohama: "An Evaluation of Statistical Properties of Pseudo-Random Numbers Generated by One-Dimensional Maps" Proceedings of NOLTA'93. 971-974 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "On the Realization of Prescribed Sets of Equilibrium Points of One-Dimensional Neural Networks with Tapered Connecting Coefficients" Proceedings of NOLTA'93. 235-238 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahasi, T.Nishi: "Realization of Equilibrium Points by Means of Completely Symmetrical Nonlinear Circuits" Memoir of the faculty of engineering Kyushu University. Vol.54. 141-160 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] N.Takahasi, T.Nishi: "On the Equilibrium Points of Hopfield-Type Neural Networks with the Cyclic Connection Matrix" Proceedings of NOLTA'94. 21-24 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishi: "Necessary and Sufficient Condition for the Basic Equation of Nonlinear Resistive Circuits Containing Ideal Diodes to Have a Unique Solution" IEICE Transaction. E76-A. 858-866 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Nishi: "Research Topics and Results on Nonlinear Circuits and Systems" IEICE Transaction. E76-A. 1077-1086 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Kawane: "An Analysis of Nonlinear Resistive Circuits Including Ideal Diodes by the Use of Scattering Matrix" KITE Journal. Vol.4. 45-51 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Kawane: "An Algorithm for Solving an Equation of Resistive Circuits Including Ideal Diodes as a Nonlinear Resistor" Proceedings of JTC-CSCC'93. Vol.1. 1-5 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Takahashi: "Realization of Certain Sets of Equilibrium Points by a Simple Neural Network" Proceedings of JTC-CSCC'93. Vol.1. 792-796 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Nishi: "Necessary and Sufficient Condition for Nonlinear Resistive Circuits Containing Ideal Diodes to have a Unique Solution" Proceedings of ECCTD'93. 1661-1666 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Takahasi: "Equilibrium Points of Mutually Coupled Symmetrical Neural Networks" Proceedings of ECCTD'93. 1059-1064 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Oohama: "An Evaluation of Statistical Properties of Pseudo-Random Numbers Generated by One-Dimensional Maps" Proceedings of NOLTA'93. 971-974 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] T,Nishi: "On the Realization of Prescribed Sets of Equilibrium Points of One-Dimensional Neural Networks with Tapered Connecting Coefficients" Proceedings of NOLTA'93. 235-238 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Takahasi,T.Nishi: "Realization of Equilibrium Points by Means of Completely Symmetrical Nonlinear Circuits" 九州大学工学部紀要. Vol.54. 141-160 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Takahasi,T.Nishi: "On the Equilibrium Points of Hopfield-Type Neural Networks with the Cyclic Connection Matrix" Proceedings of NOLTA'94. 21-24 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tetsuo Nishi: "Necessary and Sufficient Condition for the Basic Equation of Nonlinear Resistive Circuits Containing Ideal Diodes to Have a Unique Solution" IEICE Transaction. Vol.E76-A. 858-866 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tetsuo Nishi: "Research Topics and Results on Nonlinear Circuits and Systems" IEICE Transaction. Vol.E76-A. 1077-1086 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yuji Kawane: "An Analysis of Nonlinear Resistive Circuits Including Ideal Diodes by the Use of Scattering Matrix" KITE Journal of Electronics Engineering. Vol.4. 45-51 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yuji Kawane: "An Algorithm for Solving an Equation of Resistive Circuits Including Ideal Diodes as a Nonlinear Resistor" Proc.JTC-CSCC'93. Vol.1. 1-5 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Norikazu Takahashi: "Realization of Certain Sets of Equilibrium Points by a Simple Neural Network" Proc.JTC-CSCC'93. Vol.2. 792-796 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tetsuo Nishi: "Necessary and Sufficient Condition for Nonlinear Resistive Circuits Containing Ideal Diodes to have a Unique Solution" Proc.ECCTD'93. 1661-1666 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Norikazu Takahashi: "Equilibrium Points of Mutually Coupled Symmetrical Neural Networks" Proc.ECCTD'93. 1059-1064 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 大〓靖匡: "加法型多重アクセス通信路の最大誤り容量域" 九州大学工学集報. 66. 505-508 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 大〓靖匡: "相関を有するガウス性無記憶情報源に対する多端子伝送率・歪理論" 第16回情報理論とその応用シンポジウム予稿集. 91-94 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 大〓靖匡: "加法型多重アクセス通信路に対する強逆定理" 九州大学工学集報. 66. 633-639 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yasutada Oohama: "An Evaluation of Statistical Properties of Pseudo-Random Numbers Generated by One-Dimensional Maps" Proc.NOLTA'93. Vol.3. 971-974 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Tetsuo Nishi: "On the Realization of Prescribed Sets of Equilibrium Points of One-Dimensional Neural Networks with Tapered Connecting Coefficients" Proc.NOLTA'93. Vol.1. 235-238 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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