Global convergence of neural networks with discontinuous neuron activations
Global convergence of neural networks with discontinuous neuron activations
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DOI：
10.1109/tcsi.2003.818614
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发表时间：
2003-11
影响因子：
5.1
通讯作者：
M. Forti;P. Nistri
中科院分区：
文献类型：
--
作者：
M. Forti;P. Nistri
本文介绍了一类神经网络，其中神经元的激活是由不连续函数建模。神经网络具有附加的互连结构，并且它们包括作为特定情况的Hopfield神经网络（HNN）和标准细胞神经网络（CNN），在HNN和CNN具有无限增益的神经元的限制情况下。导出了保证存在唯一平衡点和唯一输出平衡点的条件，这些平衡点对神经网络的状态和输出轨迹分别具有全局吸引力。这些条件，这是适用于一般的非对称神经网络，是基于李雅普诺夫对角稳定的神经元互连矩阵的概念，他们可以被认为是作为一个推广的不连续的情况下建立的神经网络具有光滑的神经元激活。此外，通过适当地利用滑动模式的存在下，获得了全新的条件，确保在有限时间内的全局收敛，其中收敛时间可以很容易地估计的基础上的相关神经网络参数。本文的分析采用了由Filippov引入的右端不连续的微分方程理论的结果。特别是，全局收敛性的微分包含的单调轨迹的概念的基础上，使用一个类似李雅普诺夫的方法。
The paper introduces a general class of neural networks where the neuron activations are modeled by discontinuous functions. The neural networks have an additive interconnecting structure and they include as particular cases the Hopfield neural networks (HNNs), and the standard cellular neural networks (CNNs), in the limiting situation where the HNNs and CNNs possess neurons with infinite gain. Conditions are derived which ensure the existence of a unique equilibrium point, and a unique output equilibrium point, which are globally attractive for the state and the output trajectories of the neural network, respectively. These conditions, which are applicable to general nonsymmetric neural networks, are based on the concept of Lyapunov diagonally-stable neuron interconnection matrices, and they can be thought of as a generalization to the discontinuous case of previous results established for neural networks possessing smooth neuron activations. Moreover, by suitably exploiting the presence of sliding modes, entirely new conditions are obtained which ensure global convergence in finite time, where the convergence time can be easily estimated on the basis of the relevant neural-network parameters. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. In particular, global convergence is addressed by using a Lyapunov-like approach based on the concept of monotone trajectories of a differential inclusion.