Deep neural networks

Notation

$l = 4$ layers $n^{[l]} = \text{# of units in layer } l$

$n^{[0]} = 3$ $n^{[1]} = 5$ $n^{[2]} = 5$ $n^{[3]} = 3$ $n^{[4]} = n^{[l]} = 1$

Input: $a^{[l - 1]}$

Output: $a^{[l]}$, cache $(z^{[l]})$ and $W^{[l]}$, $b^{[l]}$

$Z^{[l]} = W^{[l]} A^{[l-1]} + b^{[l]}$

$A^{[l]} = g^{[l]}(Z^{[l]})$

$A^{[0]}$ is input set.

Input: $da^{[l]}$

Output: $da^{[l-1]}, dW^{[l]}, db^{[l]}$

$dz^{[l]} = da^{[l]} * g'^{[l]}(z^{[l]})$

$dW^{[l]} = dz^{[l]} * a^{[l-1]}$

$db^{[l]} = dz^{[l]}$

$da^{[l-1]} = W^{[l]^T} * dz^{[l]}$