  Knowledge distillation is a generalized logits matching technique for model
compression. Their equivalence is previously established on the condition of
$\textit{infinity temperature}$ and $\textit{zero-mean normalization}$. In this
paper, we prove that with only $\textit{infinity temperature}$, the effect of
knowledge distillation equals to logits matching with an extra regularization.
Furthermore, we reveal that an additional weaker condition --
$\textit{equal-mean initialization}$ rather than the $\textit{zero-mean
normalization}$ already suffices to set up the equivalence. The key to our
proof is we realize that in neural networks with the cross-entropy loss and
softmax activation, the mean of back-propagated gradient on logits always keeps
zero.
