每层3个节点的神经网络对连续函数的逼近

Approximation of continuous functions by neural networks with three nods at each layer

主要研究了多层前馈人工神经网络对Rd上连续函数的逼近,证得每层3个节点的n(n+d-1/d-1)层前馈人工神经网络可以按任意给定的精度逼近任一总次数为n的d元代数多项式,并给出d=1时的实例验证.此外,由Weierstrass定理,所构造的前馈人工神经网络可以按任意给定的精度逼近连续函数.最后,将该结论推广到多维输出的情形.

Mainly discussed the approximation of continuous functions on Rd by the multilayer feed-forward arTIF;%95%94icial neural network and proves that n(n+d-1/d-1) layers neural networks with three nodes at each layer could approximate any d-dimensional algebraic polynomial of degree n with arbitrary given accuracy.An example was given to illustrate the conclusion in the case of d=1.By the Weierstrass theorem,the result is proved that the constructed neural network can approximate any continuous functions with ar...