APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD NETWORKS
APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD NETWORKS
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DOI：
10.1016/0893-6080(91)90009-t
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发表时间：
1991-01-01
期刊：
影响因子：
7.8
通讯作者：
HORNIK, K
中科院分区：
文献类型：
--
作者：
HORNIK, K
我们表明，标准的多层前馈网络少到一个单一的隐藏层和任意有界和非常数激活函数是通用的逼近L（p）（μ）的性能标准，对于任意有限的输入环境措施μ，只要有足够多的隐藏单元可用。如果激活函数是连续的、有界的和非常数的，则连续映射可以在紧输入集上一致学习。我们还给出了非常一般的条件，确保具有足够光滑的激活函数的网络能够任意精确地逼近函数及其导数。
We show that standard multilayer feedforward networks with as few as a single hidden layer and arbitrary bounded and nonconstant activation function are universal approximators with respect to L(p)(mu) performance criteria, for arbitrary finite input environment measures mu, provided only that sufficiently many hidden units are available. If the activation function is continuous, bounded and nonconstant, then continuous mappings can be learned uniformly over compact input sets. We also give very general conditions ensuring that networks with sufficiently smooth activation functions are capable of arbitrarily accurate approximation to a function and its derivatives.