Deep Neural Networks have achieved huge success at a wide spectrum of applications from language modeling, computer vision to speech recognition. However, nowadays, good performance alone is not enough to satisfy the needs of practical deployment where interpretability is demanded for cases involving ethics and mission critical applications. The complex models of Deep Neural Networks make it hard to understand and reason the predictions, which hinders its further progress. To tackle this problem, we apply the Knowledge Distillation technique to distill Deep Neural Networks into decision trees in order to attain good performance and interpretability simultaneously. We formulate the problem at hand as a multi-output regression problem and the experiments demonstrate that the student model achieves significantly better accuracy performance (about 1 to 5 ) than vanilla decision trees at the same level of tree depth. The experiments are implemented on the TensorFlow platform to make it scalable to big datasets. To the best of our knowledge, we are the first to distill Deep Neural Networks into vanilla decision trees on multi-class datasets.
Perhaps the most related work is the model in @cite_26 which uses a type of soft decision tree to mimic the input-output functions of a trained DNN. This soft decision tree produces hierarchical decisions, which is more easier to interpret than DNN that relies on hierarchical features. It is modeled based on hierarchical mixture of experts and trained with gradient descent. The way they design the soft decision tree is quite similar to @cite_42 . Knowledge distillation was then used to improve the soft decision tree's accuracy. The difference between their approach and ours is that we use vanilla decision tree as the student model while their student model is the soft decision tree which has similar architecture with neural networks and could be more easily adapted to the original knowledge distillation framework.
@cite_26 @cite_42
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We present Deep Neural Decision Forests - a novel approach that unifies classification trees with the representation learning functionality known from deep convolutional networks, by training them in an end-to-end manner. To combine these two worlds, we introduce a stochastic and differentiable decision tree model, which steers the representation learning usually conducted in the initial layers of a (deep) convolutional network. Our model differs from conventional deep networks because a decision forest provides the final predictions and it differs from conventional decision forests since we propose a principled, joint and global optimization of split and leaf node parameters. We show experimental results on benchmark machine learning datasets like MNIST and ImageNet and find on-par or superior results when compared to state-of-the-art deep models. Most remarkably, we obtain Top5-Errors of only 7.84 6.38 on ImageNet validation data when integrating our forests in a single-crop, single seven model GoogLeNet architecture, respectively. Thus, even without any form of training data set augmentation we are improving on the 6.67 error obtained by the best GoogLeNet architecture (7 models, 144 crops). We discuss a novel decision tree architecture with soft decisions at the internal nodes where we choose both children with probabilities given by a sigmoid gating function. Our algorithm is incremental where new nodes are added when needed and parameters are learned using gradient-descent. We visualize the soft tree fit on a toy data set and then compare it with the canonical, hard decision tree over ten regression and classification data sets. Our proposed model has significantly higher accuracy using fewer nodes. We present a novel approach to enrich classification trees with the representation learning ability of deep (neural) networks within an end-to-end trainable architecture. We combine these two worlds via a stochastic and differentiable decision tree model, which steers the formation of latent representations within the hidden layers of a deep network. The proposed model differs from conventional deep networks in that a decision forest provides the final predictions and it differs from conventional decision forests by introducing a principled, joint and global optimization of split and leaf node parameters. Our approach compares favourably to other state-of-the-art deep models on a large-scale image classification task like ImageNet. Often the best performing deep neural models are ensembles of multiple base-level networks. Unfortunately, the space required to store these many networks, and the time required to execute them at test-time, prohibits their use in applications where test sets are large (e.g., ImageNet). In this paper, we present a method for compressing large, complex trained ensembles into a single network, where knowledge from a variety of trained deep neural networks (DNNs) is distilled and transferred to a single DNN. In order to distill diverse knowledge from different trained (teacher) models, we propose to use adversarial-based learning strategy where we define a block-wise training loss to guide and optimize the predefined student network to recover the knowledge in teacher models, and to promote the discriminator network to distinguish teacher vs. student features simultaneously. The proposed ensemble method (MEAL) of transferring distilled knowledge with adversarial learning exhibits three important advantages: (1) the student network that learns the distilled knowledge with discriminators is optimized better than the original model; (2) fast inference is realized by a single forward pass, while the performance is even better than traditional ensembles from multi-original models; (3) the student network can learn the distilled knowledge from a teacher model that has arbitrary structures. Extensive experiments on CIFAR-10 100, SVHN and ImageNet datasets demonstrate the effectiveness of our MEAL method. On ImageNet, our ResNet-50 based MEAL achieves top-1 5 21.79 5.99 val error, which outperforms the original model by 2.06 1.14 .