事件触发突触反馈解析神经网络的全局收敛性
Global Convergence of Analytic Neural Networks with Event-triggered Synaptic Feedbacks
摘要：
本文研究了一类具有事件触发规则的解析神经网络的收敛性。该模型具有一般性，并将Hopfield神经网络作为其特例。事件触发规则有效地减少了神经元突触之间的信息传输频率。每个神经元的突触反馈在其最近的触发时间基于其邻居的输出保持恒定值，但是直到该神经元的下一个触发时间才改变，该下一个触发时间由特定标准经由其邻居信息确定。证明了在这种事件触发规则下解析神经网络是完全稳定的。主要的证明技巧是利用$Ł$ ojasiewicz不等式证明轨迹长度的有限性。通过排除Zeno行为验证了该事件触发规则的实现。数值例子来说明理论结果，并提出了网络动力学的优化能力。
英文摘要：
In this paper, we investigate convergence of a class of analytic neural networks with event-triggered rule. This model is general and include Hopfield neural network as a special case. The event-trigger rule efficiently reduces the frequency of information transmission between synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of its neighbours at its latest triggering time but changes until the next triggering time of this neuron that is determined by certain criterion via its neighborhood information. It is proved that the analytic neural network is completely stable under this event-triggered rule. The main technique of proof is the $Ł$ojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the optimisation capability of the network dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
