Knowledge distillation aims to transfer useful information from a teacher network to a student network, with the primary goal of improving the student's performance for the task at hand. Over the years, there has a been a deluge of novel techniques and use cases of knowledge distillation. Yet, despite the various improvements, there seems to be a glaring gap in the community's fundamental understanding of the process. Specifically, what is the knowledge that gets distilled in knowledge distillation? In other words, in what ways does the student become similar to the teacher?

Knowledge distillation aims to transfer useful information from a teacher network to a student network, with the primary goal of improving the student's performance for the task at hand. Over the years, there has a been a deluge of novel techniques and use cases of knowledge distillation. Yet, despite the various improvements, there seems to be a glaring gap in the community's fundamental understanding of the process. Specifically, what is the knowledge that gets distilled in knowledge distillation? In other words, in what ways does the student become similar to the teacher? Does it start to localize objects in the same way? Does it get fooled by the same adversarial samples? Does its data invariance properties become similar? Our work presents a comprehensive study to try to answer these questions. We show that existing methods can indeed indirectly distill these properties beyond improving task performance. We further study why knowledge distillation might work this way, and show that our findings have practical implications as well.

Revoking personal private data is one of the basic human rights, which has already been sheltered by several privacy-preserving laws in many countries. However, with the development of data science, machine learning and deep learning techniques, this right is usually neglected or violated as more and more patients' data are being collected and used for model training, especially in intelligent healthcare, thus making intelligent healthcare a sector where technology must meet the law, regulations, and privacy principles to ensure that the innovation is for the common good. In order to secure patients' right to be forgotten, we proposed a novel solution by using auditing to guide the forgetting process, where auditing means determining whether a dataset has been used to train the model and forgetting requires the information of a query dataset to be forgotten from the target model. We unified these two tasks by introducing a new approach called knowledge purification. To implement our solution, we developed AFS, a unified open-source software, which is able to evaluate and revoke patients' private data from pre-trained deep learning models. We demonstrated the generality of AFS by applying it to four tasks on different datasets with various data sizes and architectures of deep learning networks. The software is publicly available at \url{https://github.com/JoshuaChou2018/AFS}.

The lack of crisp mathematical models that capture the structure of real-world data sets is a major obstacle to the detailed theoretical understanding of deep neural networks. Here, we first demonstrate the effect of structured data sets by experimentally comparing the dynamics and the performance of two-layer networks trained on two different data sets: (i) an unstructured synthetic data set containing random i.i.d. inputs, and (ii) a simple canonical data set containing MNIST images. Our analysis reveals two phenomena related to the dynamics of the networks and their ability to generalise that only appear when training on structured data sets. Second, we introduce a generative model for data sets, where high-dimensional inputs lie on a lower-dimensional manifold and have labels that depend only on their position within this manifold. We call it the hidden manifold model and we experimentally demonstrate that training networks on data sets drawn from this model reproduces both the phenomena seen during training on MNIST.