Chandra Pravin, Singh Yogesh
School of Information Technology, GGS Indraprastha University, Delhi-110006, India.
IEEE Trans Neural Netw. 2004 Nov;15(6):1350-66. doi: 10.1109/TNN.2004.831198.
Sigmoidal feedforward artificial neural networks (FFANNs) have been established to be universal approximators of continuous functions. The universal approximation results are summarized to identify the function sets represented by the sigmoidal FFANNs with the universal approximation properties. The equicontinuous properties of the identified sets is analyzed. The equicontinuous property is related to the fault tolerance of the sigmoidal FFANNs. The generally used arbitrary weight sigmoidal FFANNs are shown to be nonequicontinuous sets. A class of bounded weight sigmoidal FFANNs is established to be equicontinuous. The fault-tolerance behavior of the networks is analyzed and error bounds for the induced errors established.
Sigmoid型前馈人工神经网络（FFANNs）已被证明是连续函数的通用逼近器。总结了通用逼近结果，以识别具有通用逼近特性的Sigmoid型FFANNs所表示的函数集。分析了所识别集合的等度连续性质。等度连续性质与Sigmoid型FFANNs的容错性有关。结果表明，一般使用的任意权重Sigmoid型FFANNs是非等度连续集。建立了一类有界权重Sigmoid型FFANNs为等度连续的。分析了网络的容错行为，并建立了诱导误差的误差界。
