Distilling the Knowledge in a Neural Network公式2推导

$推导：$
$\begin{array}{rl}\frac{\partial C}{\partial z_i}& =\sum _{j=1}^N\frac{\partial C}{\partial q_j}\frac{\partial q_j}{\partial z_i}\\ & =\frac{\partial C}{\partial q_i}\frac{\partial q_i}{\partial z_i}+\sum _{j=1,j\ne i}^N\frac{\partial C}{\partial q_j}\frac{\partial q_j}{\partial z_i}\\ & =\frac{1}{T}[p_i(q_i-1)+\sum _{j=1,j\ne i}^N{p}_j{q}_i]\\ & =\frac{1}{T}(q_i-p_i)\end{array}$