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 tha
t 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 original $textit{zero-mean normalization}$ already suffices to set up the equivalence. The key to our proof is we realize that in modern neural networks with the cross-entropy loss and softmax activation, the mean of back-propagated gradient on logits always keeps zero.
Knowledge Distillation (KD) aims at transferring knowledge from a larger well-optimized teacher network to a smaller learnable student network.Existing KD methods have mainly considered two types of knowledge, namely the individual knowledge and the
relational knowledge. However, these two types of knowledge are usually modeled independently while the inherent correlations between them are largely ignored. It is critical for sufficient student network learning to integrate both individual knowledge and relational knowledge while reserving their inherent correlation. In this paper, we propose to distill the novel holistic knowledge based on an attributed graph constructed among instances. The holistic knowledge is represented as a unified graph-based embedding by aggregating individual knowledge from relational neighborhood samples with graph neural networks, the student network is learned by distilling the holistic knowledge in a contrastive manner. Extensive experiments and ablation studies are conducted on benchmark datasets, the results demonstrate the effectiveness of the proposed method. The code has been published in https://github.com/wyc-ruiker/HKD
