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Concept

Backward Propagation Formulation

Input:

dA[l]dA^{[l]}

For the last layer (L):

dA[L]=i=1my[1]a[1]+1y[1]1a[1]dA^{[L]} = \sum_{i=1}^{m} -\frac{y^{[1]}}{a^{[1]}} + \frac{1 - y^{[1]}}{1 - a^{[1]}}

Output:

dA[l1],dW[l],db[l]dA^{[l-1]}, dW^{[l]}, db^{[l]}

dZ[l]=dA[l]g[l](Z[l])dZ^{[l]} = dA^{[l]} g'^{[l]}(Z^{[l]})

dW[l]=1mdZ[l]A[l1]TdW^{[l]} = \frac{1}{m} dZ^{[l]} A^{[l - 1] T}

db[l]=1mdZ[l]db^{[l]} = \frac{1}{m} \sum dZ^{[l]}

dA[l1]=W[l]TdZ[l]dA^{[l - 1]} = W^{[l]T} dZ^{[l]}

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Updated 2022-11-07

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Data Science

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