STOCHASTIC DYNAMICS OF TIME-SUMMATING BINARY NEURAL NETWORKS

被引:9
作者
BRESSLOFF, PC
机构
[1] GEC-Marconi Ltd., Hirst Research Centre, Wembley, Middlesex, East Lane
来源
PHYSICAL REVIEW A | 1991年 / 44卷 / 06期
关键词
D O I
10.1103/PhysRevA.44.4005
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
An analysis is given of the stochastic dynamics of time-summating binary neural networks. Such networks have a memory or trace of their previous output activity reaching back to some initial time. Particular attention is given to a class of networks based on a discrete time version of leaky-integrator shunting networks. The stochastic dynamics is formulated as a linear Markov process describing the evolution of densities on the infinite-dimensional space of neuronal activation states. Using certain results from the theory of linear Markov operators, due to Lasota and Mackey [Probabilistic Properties of Deterministic Systems (Oxford University, Oxford, 1986); Physica D 28, 143 (1987)], conditions are derived for asymptotic stability in which the network converges to a unique limiting density. Moreover, the limiting density is shown to be a differentiable function of the parameters of the network such as the weights and decay factors. Finally, dynamical mean-field equations are derived that have periodic and chaotic solutions, implying a breaking of asymptotic stability in the thermodynamic limit.
引用
收藏
页码:4005 / 4016
页数:12
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