On student-teacher deviations in distillation: does it pay to disobey?

Knowledge distillation (KD) has been widely-used to improve the test accuracy of a ``student'' network by training the student to mimic soft probabilities of a trained "teacher" network. Yet, it has been shown in recent work that, despite being trained to fit the teacher's probabilities, the student not only significantly deviates from these probabilities, but also performs even better than the teacher. Our work aims to reconcile this seemingly paradoxical observation by characterizing the precise nature of the student-teacher deviations, and by arguing how they can co-occur with better generalization. First, through experiments on image and language data, we identify that these deviations correspond to the student systematically exaggerating the confidence levels of the teacher. Next, we theoretically and empirically establish in some simple settings that KD also exaggerates the implicit bias of gradient descent in converging faster along the top eigendirections of the data. Finally, we demonstrate that this exaggerated bias effect can simultaneously result in both (a) the exaggeration of confidence and (b) the improved generalization of the student, thus offering a resolution to the apparent paradox. Our analysis brings existing theory and practice closer by considering the role of gradient descent in KD and by demonstrating the exaggerated bias effect in both theoretical and empirical settings.