Global behavior of homogeneous random neural systems

Abstract We define a simple form of homogeneous neural network model whose characteristics are expressed in terms of probabilistic assumptions. The networks considered operate in an asynchronous manner and receive the influence of the environment in the form of external stimulations. The operation of the network is described by means of a Markovian process whose steady-statesolution yields several global measures of the network's activity. Three different types of external stimulations are investigated, which represent possible input mechanisms. The analytical results obtained concern the macroscopic viewpoint and provide a quick insight into the structure of the network's behavior.

[1]  Pierre Peretto,et al.  On the dynamics of memorization processes , 1988, Neural Networks.

[2]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[3]  D. Amit,et al.  Statistical mechanics of neural networks near saturation , 1987 .

[4]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[5]  Richard P. Lippmann,et al.  An introduction to computing with neural nets , 1987 .

[6]  S. Amari,et al.  Characteristics of Random Nets of Analog Neuron-Like Elements , 1972, IEEE Trans. Syst. Man Cybern..

[7]  Pierre Peretto,et al.  Stochastic Dynamics of Neural Networks , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[9]  B. Huberman,et al.  Dynamic behavior of nonlinear networks , 1983 .

[10]  John W. Clark,et al.  Statistical mechanics of neural networks , 1988 .

[11]  Sompolinsky,et al.  Spin-glass models of neural networks. , 1985, Physical review. A, General physics.

[12]  Marios D. Dikaiakos,et al.  Spatial Organization of Neural Networks: A Probabilistic Modeling Approach , 1987, NIPS.

[13]  E M Harth,et al.  Dynamics of neural structures. , 1970, Journal of theoretical biology.

[14]  F. Fogelman-Soulié,et al.  Random Boolean Networks , 1981 .