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Nonequilibrium statistical mechanics of neural networks

神经网络的非平衡统计力学

基本信息

批准号：
02640289
负责人：
SHIINO Masatoshi
金额：
$ 1.54万
依托单位：
Tokyo Institute of Technology Faculty of Science
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

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.

从吸引子网络平衡态和动态态的统计行为角度研究了联想记忆神经网络的性质。我们关注了网络行为的统计力学方面，并充分利用了相变的概念。特别强调的是对与生物神经网络相关的模型系统的分析，由于系统缺乏能量函数，非平衡统计力学的使用是必不可少的。我们得到了以下结果：1。从非平衡相变的角度探讨了具有不对称突触连接的随机Ising自旋神经网络丰富的动力学行为，这可以看作是热力学相变的直接推广。阐明了伊辛自旋与模拟神经网络的关系，并从存储容量和伪态数密度两方面比较了两种网络的性能。我们提出了一种新的方法，我们称之为自洽信噪分析（SCSNA），它能够评估具有一般类型传递函数的模拟网络的存储容量。验证了该方法的有效性和有效性。将SCSNA应用于具有非单调传递函数的模拟网络的存储容量评估中，存储容量得到了显著提高，并产生了一种新的检索状态，保证了在Hebb型局部学习规则下记忆检索的准确性。这一新发现意味着使用具有某种非单调传递函数的模拟网络可以显著提高网络作为联想记忆的性能。