第四周—深层神经网络

一、深层神经网络

神经网络符号：

输入数据层：layer0，不包括在层数中

n^[l]：第l层包含的神经元数目

二、前向和反向传播

z^[l] = w^[l] * a^[l-1] + b^[l]

a^[l] = g^[l](z^[l])

向量化：

Z^[l] = W^[l] * A^[l-1] + b^[l]

A^[l] = g^[l](Z^[l])

第l层反向传播：

输入：da^[l]

输出：da^[l-1]   dw^[l]   db^[l]

dz^[l] = da^[l] * g^[l]‘(z^[l])

dw^[l] = dz^[l] * a^[l-1]

db^[l] = dz^[l]

da^[l-1]  = w^[l]T * dz^[l]

向量化：

dZ^[l] = dA^[l] * g^[l]‘(Z^[l])

dW^[l] = 1/m dZ^[l] * A^[l-1]T

db^[l] = 1/m np.sum( dz^[l] ,axis=1, keepdim=TRUE) 

dA^[l-1]  = W^[l]T * dZ^[l]