Unpacking the Gap Box Against Data-Free Knowledge Distillation
Data-free knowledge distillation (DFKD) improves the student model (S) by mimicking the class probability from a pre-trained teacher model (T) without training data. Under such setting, an ideal scenario is that T can help generate ”good” samples from a generator (G) to maximally benefit S. However, existing arts suffer from the non-ideal generated samples under the disturbance of the gap ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e. , either too large or small) between the class probabilities of T and S; for example, the generated samples with too large gap may exhibit <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">excessive information for S, while too small gap leads to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">limited knowledge in the samples, resulting into the poor generalization. Meanwhile, they fail to judge the ”goodness” of the generated samples for S since the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fixed T is not necessarily ideal. In this paper, we aim to answer <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">what is inside the gap box ; together with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">how to yield ”good” generated samples for DFKD? To this end, we propose a <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gap - <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S ensitive <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S ample <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G eneration (GapSSG) approach, by revisiting the empirical distilled risk from a data-free perspective, which confirms the existence of an ideal teacher (T $^*$ ), while theoretically implying: (1) the gap disturbance originates from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mismatch between T and T $^*$ , hence the class probabilities of T enable the approximation to those of T $^*$ ; and (2) ”good” samples should maximally benefit S via T's class probabilities, owing to unknown T $^*$ . To this end, we unpack the gap box between T and S as two findings: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inherent gap to perceive T and T $^*$ ; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">derived gap to monitor S and T $^*$ . Benefiting from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">derived gap that focuses on the adaptability of generated sample to S, we attempt to track student's training route (a series of training epochs) to capture the category distribution of S; upon which, a regulatory factor is further devised to approximate T $^*$ over <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inherent gap, so as to generate ”good” samples to S. Furthermore, during the distillation process, a sample-balanced strategy comes up to tackle the overfitting and missing knowledge issues between the generated partial and critical samples by training G. The theoretical and empirical studies verify the advantages of GapSSG over the state-of-the-arts. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Our code is available at https://github.com/hfutqian/GapSSG .