The local minima-free condition of feedforward neural networks for outer-supervised learning
The local minima-free condition of feedforward neural networks for outer-supervised learning
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DOI：
10.1109/3477.678658
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发表时间：
1998-06
期刊：
影响因子：
--
通讯作者：
De-shuang Huang
中科院分区：
文献类型：
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作者：
De-shuang Huang
利用嵌入子空间方法研究了基于批处理学习的外监督前馈神经网络(FNN)的局部无极小条件。证明了只有满足隐含神经元个数不少于训练样本个数的条件(充分但不必要)时，网络必然以零代价收敛到全局最小点，且外监督信号矩阵的值域空间包含在隐出输出矩阵的值域空间是误差面无局部极小值的充要条件。此外，在隐含神经元个数小于训练样本个数、大于输出神经元个数的情况下，证明了在充分选取第一层权值的情况下，误差面也只存在零代价的全局极小值。
In this paper, the local minima-free conditions of the outer-supervised feedforward neural networks (FNN) based on batch-style learning are studied by means of the embedded subspace method. It is proven that only if the rendition that the number of the hidden neurons is not less than that of the training samples, which is sufficient but not necessary, is satisfied, the network will necessarily converge to the global minima with null cost, and that the condition that the range space of the outer-supervised signal matrix is included in the range space of the hidden output matrix Is sufficient and necessary condition for the local minima-free in the error surface. In addition, under the condition of the number of the hidden neurons being less than that of the training samples and greater than the number of the output neurons, it is demonstrated that there will also only exist the global minima with null cost in the error surface if the first layer weights are adequately selected.