标题： 忆阻器神经网络中的收敛权重和激活动力学 显示英文标题

标题： Convergent Weight and Activation Dynamics in Memristor Neural Networks

摘要： 动态反馈神经网络（NNs），如Cohen-Grossberg、Hopfield和细胞NNs，其收敛性长期以来一直是NN理论的支柱。 确实，在存在多个稳定平衡点（EPs）的情况下实现收敛对于实现内容寻址存储器和实时解决其他信号处理任务至关重要。 使用收敛NN有两种典型方式，即：a）在保持权重和输入固定的情况下让激活值演化（激活动力学），或b）在保持激活值固定的情况下调整权重（权重动力学）。 正如Hirsch的一篇开创性论文中所指出的，还有另一种有趣的可能性，即在同时运行激活动力学的同时让神经元互连权重演化（权重-激活动力学）。 权重-激活动力学之所以重要，还因为与另外两种类型相比，它更符合神经系统的建模。 本文首次以系统的方式分析了忆阻器反馈动态NN类的权重-激活动力学的收敛特性，开辟了新的研究领域。 主要结果是，在对忆阻器互连结构做出适当假设的情况下，解（权重和激活值）会收敛到一个EP，最多只有一种测度为零的初始条件集合除外。 该结果包括NN具有多个稳定EP的最重要情况。 显示英文摘要

摘要： Convergence of dynamic feedback neural networks (NNs), as the Cohen-Grossberg, Hopfield and cellular NNs, has been for a long time a workhorse of NN theory. Indeed, convergence in the presence of multiple stable equilibrium points (EPs) is crucial to implement content addressable memories and solve several other signal processing tasks in real time. There are two typical ways to use a convergent NN, i.e.: a) let the activations evolve while maintaining fixed weights and inputs (activation dynamics) or b) adapt the weights while maintaining fixed activations (weight dynamics). As remarked in a seminal paper by Hirsch, there is another interesting possibility, i.e., let the neuron interconnection weights evolve while simultaneously running the activation dynamics (weight-activation dynamics). The weight-activation dynamics is of importance also because it is more plausible than the other two types for modeling neural systems. The paper breaks new ground by analyzing for the first time in a systematic way the convergence properties of the weight-activation dynamics for a class of memristor feedback dynamic NNs. The main result is that, under suitable assumptions on the structure of the memristor interconnections, the solutions (weights and activations) converge to an EP, except at most for a set of initial conditions with zero measure. The result includes the most important case where the NN has multiple stable EPs.