• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Nonequilibrium statistical mechanics of neural networks

Research Project

Project/Area Number 02640289
Research Category

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

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionTokyo Institute of Technology Faculty of Science

Principal Investigator

SHIINO Masatoshi  Tokyo Inst.Tech. Science Research Associate, 理学部, 助手 (60134813)

Co-Investigator(Kenkyū-buntansha) FUKAI Tomoki  Tokai Univ. Engineering Assistant professor, 工学部, 講師 (40218871)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1991: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1990: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsAnalog Networks / Hopfield Model / Storage Capacity / Self-Consistent Signal Noise Analysis / Asymmetric Synaptic Connection / Nonequilibrium Phase Transition / Chaotic Neural Networks / Spurious States / アナログニュ-ラルネット / ホップフィ-ルドモデル / カオスニュ-ラルネット / 準安定状態数
Research Abstract

We have studied the properties of neural networks of associative memory from the view point of the statistical behavior of equilibrium and dynamical states of attractor networks. We have concerned with the statistical mechanical aspect of the network behaviors and made full use of the concept of phase transitions. A particular emphasis has been put on the analysis of model systems having relevance to biological neural networks for which use of nonequilibrium statistical mechanics is indispensable due to the lack of energy functions of the systems. We have obtained the following results:
1.Rich dynamical behaviors of stochastic Ising spin neural networks with asymmetric synaptic connections have been explored in the light of nonequilibrium phase transitions, which can be viewed as a direct generalization of the thermodynamic phase transitions.
2.The relationship between Ising spin and analog neural networks has been elucidated and comparison of the network performances between the two networks has been made in terms of the storage capacity and the number density of the spurious states.
3.A new method we refer to as "Self-consistent signal-to-noise analysis"(SCSNA) has been proposed, which is capable of evaluating the storage capacity of analog networks with a general type of transfer functions. The validity and powerfulness of the method has been confirmed.
4.Applications of the SCSNA to the evaluation of the storage capacity of analog networks with nonmonotonic transfer functions has led to a remarkable enhancement of the storage capacity and the occurrence of a novel type of retrieval states ensuring errorless memory retrieval under the local learning rule of Hebb type. The new finding means that using analog networks with a certain type of nonmonotonic transfer functions considerably improves network performances as associative memory.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] M.Shiino: "Nonlinear master equation approach to asymmetrical neural networks of the Hopfield-Hemmen type" J.Phys.Soc.Jpn.58. 763-766 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H.Nishimori: "Retrieval of spatio-temporal sequence in asynchronous neural networks" Phys.Rev.A. 41. 3346-3354 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Stochastic analyses of the dynamics of generalired Little-Hopfield-Hemmen type neural networks" J.Stat.Phys.59. 1051-1075 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai: "Asymmetric neural networks incorporating the Dale hypothesis and noise-driven chaos" Phys.Rev,Lett.64. 1465-1468 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Chaotic dynamics in stochastic neural networks" Int.Conf.Fuzzy Logic & Neural networks Iizuka,Japan. 595-599 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Chaotic image retrieval in Markovian asymmetric neural networks with sign-constrained syraptic couplings" J.Phys.Soc.Jpn.59. 1529-1532 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Replica-symmetric theory of the nonlinear analogue neural networks" J.Phys.A Math.Gen.23. L1009-1017 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai: "Large suppression of spurious states in neural networks of nonlinear analog neurons" Phys.Rev.A. 42. 7459-7466 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Self-consistent signal-to-noise analysis and its application to analog neural networks with asymmetric connections" J.Phys.A.Math.Gen.25. L375-381 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai: "Comparative study of spurious state distribution of analog neural networks and the Boltqmann machine" J.Phys.A Math.Gen.25. 2873-2887 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai: "Study of self-inhibited analogue neural networks using the self-consistent signal-to-noise analysis" J.Phys.A Math.Gen.25. 4799-4811 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage copacity" Phys.Rev.E.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 椎野 正寿: "ニューラルネットワークの統計力学とカオス 「ニューラルシステムにおけるカオス」(合原 一幸編著)第6章" 東京電機大学出版, 55 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino,H.Nishimori,and M.Ono: "Nonlinear master equation approach to asymmetrical neural networks of the Hopfield-Hemmen type" J.Phys.Soc.Jpn. 58. 763-766 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H.Nishimori,T.Nakamura,and M.Shiino: "Retrieval of spatio-temporal sequence in asynchronous neural networks" Phys.Rev,A. 41. 3346-3354 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Stochastic analyses of the dynamics of generalized Little-Hopfield-Hemmen type neural networks" J.Stat.Phys. 59. 1051-1075 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai and M.Shiino: "Asymmetric neural networks incorporating the Dale hypothesis and noise-driven chaos" Phys.Rev.Lett. 64. 1465-1468 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino and T.Fukai: "Chaotic image retrieval in Markovian asymmetric neural networks with sign-constrained synaptic couplings" J.Phys.Soc.Jpn. 59. 1529-1532 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino and T.Fukai: "Chaotic dynamics in stochastic neural networks" Int.Conf.Fuzzy Logic&Neural networks(Iizuka,Japan). 595-599 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino and T.Fukai: "Replica-symmetric theory of the nonlinear analogue neural networks" J.Phys.A. 23. L1009-1017 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai and M.Shiino: "Large suppression of spurious states in neural networks of nonlinear analog neurons" Phys.Rev.A. 42. 7459-7466 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino and T.Fukai: "Self-consistent signal-to-noise analysis and its application to analog neural networks with asymmetric connections" J.Phys.A Math. Gen.25. L375-381 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Fukai and M.Shiino: "Comparative study of spurious state distribution of analog neural networks and the Boltzman machine" J.Phys.A Math. Gen.25. 2873-2887 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Fukai and M Shiino: "Study of self-inhibited analogue neural networks using the self-consistent signal-to-noise analysis" J.Phys.A Math. Gen.25. 4799-4811 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Shiino and T. Fukai: "Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage capacity"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M. Shiino and T. Fukai: "Onset of "super retrieval phase" and enhancement of the storage capacity in neural networks of nonmonotonic neurons"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] M.Shiino: "Selfーconsistent signalーtoーnoise analysis and its application to analog neural networks with asymmetric connections" J.Phys.A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Fukai: "Comparative study of spurious state distribution of analog neural networks and the Boltgmann machine" J.Phys.A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Fukai: "Study of selfーinhibited analog neural networks using the selfーconsistant signalーtoーnoise analysis" J.Phys.A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Shiino: "Storage capacity of analog neural networks: Effect of selfーcouplings" Phys.Res.A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Shiino: "Chaotic dynamics in oscillator neural networks" Phys.Rev.A. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 椎野 正寿(分担): "ニュ-ラルネットの統計力学とカオスinニュ-ラルシステムにおけるカオス" 東京電機大学出版, (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Shiino: "Replicaーsymmetric theory of the nonlinear analogue neural networks" J.Phys.A Math.Gen.23. L1009-L1017 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Fukai: "Large suppression of spurious states in neural networks of nonlinear analog neurons" Phys.Rev.A. 42. 7459-7466 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.Shiino: "Selfーconsistent signalーtoーnoise analysis and its application to analog neural networks with asymmetric connection" Phys.Rev.Lett. (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.Shiino: "Chaotic dynamics in stochastic neural networks" Int.Conf.Fuzzy Logic & Neural Networks Iizuka,Japan. 595-599 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Fukai: "Comparative Studies of Analog Neural Network and Boltzmann Machine" J.Phys.A.Math.Gen.(1991)

    • Related Report
      1990 Annual Research Report

URL: 

Published: 1990-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi