  Knowledge Distillation (KD) has proven effective for compressing large
teacher models into smaller student models. While it is well known that student
models can achieve similar accuracies as the teachers, it has also been shown
that they nonetheless often do not learn the same function. It is, however,
often highly desirable that the student's and teacher's functions share similar
properties such as basing the prediction on the same input features, as this
ensures that students learn the 'right features' from the teachers. In this
work, we explore whether this can be achieved by not only optimizing the
classic KD loss but also the similarity of the explanations generated by the
teacher and the student. Despite the idea being simple and intuitive, we find
that our proposed 'explanation-enhanced' KD (e$^2$KD) (1) consistently provides
large gains in terms of accuracy and student-teacher agreement, (2) ensures
that the student learns from the teacher to be right for the right reasons and
to give similar explanations, and (3) is robust with respect to the model
architectures, the amount of training data, and even works with 'approximate',
pre-computed explanations.
