How to obtain a model with good interpretability and performance has always been an important research topic. In this paper, we propose rectified decision trees (ReDT), a knowledge distillation based decision trees rectification with high interpretability, small model size, and empirical soundness. Specifically, we extend the impurity calculation and the pure ending condition of the classical decision tree to propose a decision tree extension that allows the use of soft labels generated by a well-trained teacher model in training and prediction process. It is worth noting that for the acquisition of soft labels, we propose a new multiple cross-validation based method to reduce the effects of randomness and overfitting. These approaches ensure that ReDT retains excellent interpretability and even achieves fewer nodes than the decision tree in the aspect of compression while having relatively good performance. Besides, in contrast to traditional knowledge distillation, back propagation of the student model is not necessarily required in ReDT, which is an attempt of a new knowledge distillation approach. Extensive experiments are conducted, which demonstrates the superiority of ReDT in interpretability, compression, and empirical soundness.
Abstract: While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network. A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel. We introduce a novel technique for knowledge transfer, where knowledge from a pretrained deep neural network (DNN) is distilled and transferred to another DNN. As the DNN performs a mapping from the input space to the output space through many layers sequentially, we define the distilled knowledge to be transferred in terms of flow between layers, which is calculated by computing the inner product between features from two layers. When we compare the student DNN and the original network with the same size as the student DNN but trained without a teacher network, the proposed method of transferring the distilled knowledge as the flow between two layers exhibits three important phenomena: (1) the student DNN that learns the distilled knowledge is optimized much faster than the original model, (2) the student DNN outperforms the original DNN, and (3) the student DNN can learn the distilled knowledge from a teacher DNN that is trained at a different task, and the student DNN outperforms the original DNN that is trained from scratch. Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled training examples is large. But it is hard to explain why a learned network makes a particular classification decision on a particular test case. This is due to their reliance on distributed hierarchical representations. If we could take the knowledge acquired by the neural net and express the same knowledge in a model that relies on hierarchical decisions instead, explaining a particular decision would be much easier. We describe a way of using a trained neural net to create a type of soft decision tree that generalizes better than one learned directly from the training data.