Capabilities of a four-layered feedforward neural network: Four layers versus three
Capabilities of a four-layered feedforward neural network: Four layers versus three
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DOI：
10.1109/72.557662
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发表时间：
1997-03-01
影响因子：
--
通讯作者：
Tateishi, M
中科院分区：
文献类型：
--
作者：
Tamura, S;Tateishi, M
神经网络理论认为，只有当隐层单元数为无穷多时，四层前向神经网络才等价于三层前向神经网络，但在实际应用中，隐层单元数为无穷多是不切实际的，因此，研究的重点应放在隐层单元数有限的神经网络的性能上。本文证明了具有N-1个隐单元的三层前馈网络可以精确地给出任意N个输入-目标关系，并在此基础上构造了一个四层前馈网络，证明了该网络仅用（N/2）+3个隐单元就能给出任意N个输入-目标关系，且误差极小。这表明，四层前馈网络在训练数据所需的参数数量方面上级三层前馈网络。
Neural-network theorems state that only when there are infinitely many hidden units is a four-layered feedforward neural network equivalent to a three-layered feedforward neural network, In actual applications, however, the use of infinitely many hidden units is impractical, Therefore, studies should focus on the capabilities of a neural network with a finite number of hidden units, In this paper, a proof is given showing that a three-layered feedforward network with N-1 hidden units can give any N input-target relations exactly, Based on results of the proof, a four-layered network is constructed and is found to give any N Input-target relations with a negligibly small error using only (N/2)+3 hidden units. This shows that a four-layered feedforward network is superior to a three-layered feedforward network in terms of the number of parameters needed for the training data.