Buhmann J, Schulten K
Biol Cybern. 1987;56(5-6):313-27. doi: 10.1007/BF00319512.
A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless auto-associative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.
研究了一种在毫秒级动力学中具有随机元素的模型神经网络。该网络由神经元单元组成，这些单元的建模与生理神经元非常相似。网络的动态变量包括细胞电位、轴突电流和突触效能。突触的动力学遵循一种修正的赫布规则，并且如冯·德·马尔堡（1981年，1985年）所提出的，在十分之一秒的时间尺度上发展。在之前的一篇论文（布曼和舒尔滕，1986年）中，我们已经证实，由此产生的无噪声自联想网络能够完成形式联想网络（库珀，1973年；科霍宁等人，1984年，1981年；霍普菲尔德，1982年）中著名的计算任务。在本文中，我们证明了膜电位的随机波动会提高网络的性能。与确定性网络相比，有噪声的神经网络能够在更低的输入频率和更低的平均神经放电率下学习。有噪声网络的电活动与生理记录中观察到的电活动非常相似。我们还证明了联想存储会降低网络电活动所发展的相空间的有效维度。
