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输出层偏导数:首先计算损失函数相对于输出层神经元输出的偏导数。这通常直接依赖于所选的损失函数。

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在神经网络中,损失函数通常是一个复合函数,由多个层的输出和激活函数组合而成。链式法则允许我们将这个复杂的复合函数的梯度计算分解为一系列简单的局部梯度计算,从而简化了梯度计算的过程。

隐藏层偏导数:使用链式法则,将输出层的偏导数向后传播到隐藏层。对于隐藏层中的每个神经元,计算其输出相对于下一层神经元输入的偏导数,并与下一层传回的偏导数相乘,累积得到该神经元对损失函数的总偏导数。

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反向传播的目标是计算损失函数相对于每个参数的偏导数,以便使用优化算法(如梯度下降)来更新参数。

通过链式法则,我们可以从输出层开始,逐层向前计算每个参数的梯度,这种逐层计算的方式避免了重复计算,提高了梯度计算的效率。

来计算梯度,我们需要调整权重矩阵的权重。我们网络的神经元(节点)的权重是通过计算损失函数的梯度来调整的。为此

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参数偏导数:在计算了输出层和隐藏层的偏导数之后,我们需要进一步计算损失函数相对于网络参数的偏导数,即权重和偏置的偏导数。

根据问题的类型,输出层可以直接输出这些值(回归问题),或者通过激活函数(如softmax)转换为概率分布(分类问题)。

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