  Knowledge distillation involves transferring soft labels from a teacher to a
student using a shared temperature-based softmax function. However, the
assumption of a shared temperature between teacher and student implies a
mandatory exact match between their logits in terms of logit range and
variance. This side-effect limits the performance of student, considering the
capacity discrepancy between them and the finding that the innate logit
relations of teacher are sufficient for student to learn. To address this
issue, we propose setting the temperature as the weighted standard deviation of
logit and performing a plug-and-play Z-score pre-process of logit
standardization before applying softmax and Kullback-Leibler divergence. Our
pre-process enables student to focus on essential logit relations from teacher
rather than requiring a magnitude match, and can improve the performance of
existing logit-based distillation methods. We also show a typical case where
the conventional setting of sharing temperature between teacher and student
cannot reliably yield the authentic distillation evaluation; nonetheless, this
challenge is successfully alleviated by our Z-score. We extensively evaluate
our method for various student and teacher models on CIFAR-100 and ImageNet,
showing its significant superiority. The vanilla knowledge distillation powered
by our pre-process can achieve favorable performance against state-of-the-art
methods, and other distillation variants can obtain considerable gain with the
assistance of our pre-process.
