【助记Note】反向传播求导公式

已知:
$Z_{b\times m}^{[l]} = W_{b\times a}^{[l]} \cdot A_{a\times m}^{[l-1]} + \vec{v}_{b \times 1}\\ A_{b\times m}^{[l]} = g(Z^{[l]})$

$g(.)​$ 是 activation function, $dW$ 表示 $\frac{dJ}{dW}$，其他的类似。

已知 $dA^{[l]}​$，则:

$dZ^{[l]}_{b\times m} = dA^{[l]} * g'(Z^{[l]})\\ dW^{[l]}_{b\times a} = \frac{\partial \mathcal{L} }{\partial W^{[l]}} = \frac{1}{m} dZ^{[l]} A^{[l-1] T}\\ db^{[l]}_{b\times 1} = \frac{\partial \mathcal{L} }{\partial b^{[l]}} = \frac{1}{m} \sum_{i = 1}^{m} dZ^{[l](i)} (\text{横向求和})\\ dA^{[l-1]}_{a\times m} = \frac{\partial \mathcal{L} }{\partial A^{[l-1]}} = W^{[l] T} dZ^{[l]}$