Thereafter we compute the ouput error \( \boldsymbol{\delta}^L \) by computing all
$$ \delta_j^L = \sigma'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}. $$Then we compute the back propagate error for each \( l=L-1,L-2,\dots,1 \) as
$$ \delta_j^l = \sum_k \delta_k^{l+1}w_{kj}^{l+1}\sigma'(z_j^l). $$