Parallel dynamics of the fully connected Blume-Emery-Griffiths neural network

被引：7

作者：

Bollé, D

Blanco, JB

Shim, GM

机构：

[1] Katholieke Univ Leuven, Inst Theoret Fysica, B-3001 Heverlee, Belgium

[2] Chungnam Natl Univ, Dept Phys, Taejon 305764, South Korea

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2003年 / 318卷 / 3-4期

关键词：

parallel dynamics; fully connected networks; probabilistic approach;

D O I：

10.1016/S0378-4371(02)01528-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied at zero temperature using a probabilistic approach. A recursive scheme is found determining the complete time evolution of the order parameters, taking into account all feedback correlations. It is based upon the evolution of the distribution of the local field, the structure of which is determined in detail. As an illustrative example explicit analytic formula are given for the first few time steps of the dynamics. Furthermore, equilibrium fixed-point equations are derived and compared with the thermodynamic approach. The analytic results find excellent confirmation in extensive numerical simulations. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：613 / 636

页数：24

共 19 条

[1] PROPERTIES OF SPARSELY CONNECTED EXCITATORY NEURAL NETWORKS [J].

BARKAI, E ;

KANTER, I ;

SOMPOLINSKY, H .

PHYSICAL REVIEW A, 1990, 41 (02) :590-597

[2] ISING MODEL FOR LAMBDA TRANSITION AND PHASE SEPARATION IN HE-3-HE-4 MIXTURES [J].

BLUME, M ;

EMERGY, VJ ;

GRIFFITHS, RB .

PHYSICAL REVIEW A-GENERAL PHYSICS, 1971, 4 (03) :1071-+

[3] Parallel dynamics of extremely diluted symmetric Q-Ising neural networks [J].

Bollé, D ;

Jongen, G ;

Shim, GM .

JOURNAL OF STATISTICAL PHYSICS, 1999, 96 (3-4) :861-882

[4] Parallel dynamics of fully connected Q-Ising neural networks [J].

Bolle, D ;

Jongen, G ;

Shim, GM .

JOURNAL OF STATISTICAL PHYSICS, 1998, 91 (1-2) :125-153

[5] Gap structure of the local field in symmetric Q Ising neural networks [J].

Bolle, D. ;

Shim, G.M. .

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2002, 65 (06) :1-067101

[6] An optimal Q-state neural network using mutual information [J].

Bollé, D ;

Verbeiren, T .

PHYSICS LETTERS A, 2002, 297 (3-4) :156-161

[7] ON THE PARALLEL DYNAMICS OF THE Q-STATE POTTS AND Q-ISING NEURAL NETWORKS [J].

BOLLE, D ;

VINCK, B ;

ZAGREBNOV, VA .

JOURNAL OF STATISTICAL PHYSICS, 1993, 70 (5-6) :1099-1119

[8] ON POSSIBILITY OF FIRST-ORDER PHASE TRANSITIONS IN ISING SYSTEMS OF TRIPLET IONS WITH ZERO-FIELD SPLITTING [J].

CAPEL, HW .

PHYSICA, 1966, 32 (05) :966-&

[9] ORDER-PARAMETER FLOW IN THE FULLY CONNECTED HOPFIELD MODEL NEAR SATURATION [J].

COOLEN, ACC ;

SHERRINGTON, D .

PHYSICAL REVIEW E, 1994, 49 (03) :1921-1934

[10] Three-state neural network: From mutual information to the Hamiltonian [J].

Dominguez, DRC ;

Korutcheva, E .

PHYSICAL REVIEW E, 2000, 62 (02) :2620-2628

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