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Dynamics analysis and analog associative memory of networks with LT neurons

机译:LT神经元网络的动力学分析和模拟联想记忆

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The additive recurrent network structure of linear threshold neurons represents a class of biologically-motivated models, where nonsaturating transfer functions are necessary for representing neuronal activities, such as that of cortical neurons. This paper extends the existing results of dynamics analysis of such linear threshold networks by establishing new and milder conditions for boundedness and asymptotical stability, while allowing for multistability. As a condition for asymptotical stability, it is found that boundedness does not require a deterministic matrix to be symmetric or possess positive off-diagonal entries. The conditions put forward an explicit way to design and analyze such networks. Based on the established theory, an alternate approach to study such networks is through permitted and forbidden sets. An application of the linear threshold (LT) network is analog associative memory, for which a simple design method describing the associative memory is suggested in this paper. The proposed design method is similar to a generalized Hebbian approach, but with distinctions of additional network parameters for normalization, excitation and inhibition, both on a global and local scale. The computational abilities of the network are dependent on its nonlinear dynamics, which in turn is reliant upon the sparsity of the memory vectors.
机译:线性阈值神经元的累加递归网络结构代表一类生物动机模型,其中非饱和传递函数对于表示神经元活动(例如皮层神经元的活动)是必需的。本文通过为有界性和渐近稳定性建立新的和较温和的条件,同时允许多重稳定性,扩展了这种线性阈值网络动力学分析的现有结果。作为渐近稳定性的条件,已发现有界性不需要确定性矩阵对称或具有正非对角线条目。条件提出了一种设计和分析此类网络的明确方法。根据已建立的理论,通过允许和禁止的集合来研究此类网络的另一种方法。线性阈值(LT)网络的一种应用是模拟关联存储器,为此,本文提出了一种描述关联存储器的简单设计方法。所提出的设计方法类似于广义的Hebbian方法,但是在全局和局部范围上都具有用于归一化,激励和抑制的其他网络参数的区别。网络的计算能力取决于其非线性动力学,而非线性动力学又依赖于存储向量的稀疏性。

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