Distillation in neural networks using only the samples randomly drawn from a Gaussian distribution is possibly the most straightforward solution one can think of for the complex problem of knowledge transfer from one network (teacher) to the other (student). If successfully done, it can eliminate the requirement of teacher's training data for knowledge distillation and avoid often arising privacy concerns in sensitive applications such as healthcare. There have been some recent attempts at Gaussian noise-based data-free knowledge distillation, however, none of them offer a consistent or reliable solution. We identify the shift in the distribution of hidden layer activation as the key limiting factor, which occurs when Gaussian noise is fed to the teacher network instead of the accustomed training data. We propose a simple solution to mitigate this shift and show that for vision tasks, such as classification, it is possible to achieve a performance close to the teacher by just using the samples randomly drawn from a Gaussian distribution.

Figure 1: The illustrative examples for two proposed techniques: Back-imagination and Back-speech. Tiny ImageNet [Le and Y ang, 2015] serves as a compact version of the comprehensive ImageNet dataset. The Stanford Sentiment Treebank-2 (SST -2) [Socher et al., 2013] is a sentiment classification dataset Given the scarcity of datasets for understanding natural language in visual scenes, we introduce a novel textual entailment dataset, named Textual Natural Contextual Classification (TNCC). This dataset is formulated on the foundation of Crisscrossed Captions [Parekh et al., 2020], an image In this work, we employ a uniform experimental configuration for both textual entailment and sentiment classification tasks. For the image classification task, we employ the ResNet18 [He et al., 2015] model, which is considered more suitable for small datasets.

In this section, we provide further details for our data modeling. We note the difficulties of appropriately modeling the terminal variable which is a binary variable compared to the rest of the dimensions which are continuous for the environments we investigate. This is particularly challenging for "expert" datasets where early termination is rare. An immediate advantage of sampling data from a generative model is compression. As we discuss in Appendix B.3, sampling is fast ER provides high levels of dataset compression without sacrificing downstream performance in offline reinforcement learning.

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While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions.