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The local minima-free condition of feedforward neural networks forouter-supervised learning

机译:外监督学习的前馈神经网络的局部无极小条件

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摘要

In this paper, the local minima-free conditions of thenouter-supervised feedforward neural networks (FNN) based on batch-stylenlearning are studied by means of the embedded subspace method. It isnproven that only if the rendition that the number of the hidden neuronsnis not less than that of the training samples, which is sufficient butnnot necessary, is satisfied, the network will necessarily converge tonthe global minima with null cost, and that the condition that the rangenspace of the outer-supervised signal matrix is included in the rangenspace of the hidden output matrix Is sufficient and necessary conditionnfor the local minima-free in the error surface. In addition, under thencondition of the number of the hidden neurons being less than that ofnthe training samples and greater than the number of the output neurons,nit is demonstrated that there will also only exist the global minimanwith null cost in the error surface if the first layer weights arenadequately selected
机译:本文利用嵌入式子空间方法研究了基于批处理学习的外部监督前馈神经网络(FNN)的局部极小条件。有证据表明,只有满足隐式神经元的数量不少于训练样本的数量(足够但不是必需的)的前提,网络才会以零成本收敛到全局最小值。隐藏的输出矩阵的rangenspace中包含外部监督信号矩阵的rangenspace对于误差表面中的局部极小值,是充分必要的条件。此外,在隐藏神经元数量少于训练样本数量且大于输出神经元数量的条件下,证明了如果第一个隐式神经元在错误表面上也仅存在具有零成本的全局迷你人适当选择层重量

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