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We formally study how ensemble of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using knowledge distillation. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the SAME architecture, trained using the SAME algorithm on the SAME data set, and they only differ by the random seeds used in the initialization. We empirically show that ensemble/knowledge distillation in deep learning works very differently from traditional learning theory, especially differently from ensemble of random feature mappings or the neural-tangent-kernel feature mappings, and is potentially out of the scope of existing theorems. Thus, to properly understand ensemble and knowledge distillation in deep learning, we develop a theory showing that when data has a structure we refer to as multi-view, then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model by training a single model to match the output of the ensemble instead of the true label. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how the dark knowledge is hidden in the outputs of the ensemble -- that can be used in knowledge distillation -- comparing to the true data labels. In the end, we prove that self-distillation can also be viewed as implicitly combining ensemble and knowledge distillation to improve test accuracy.
Knowledge Distillation (KD) is a model-agnostic technique to improve model quality while having a fixed capacity budget. It is a commonly used technique for model compression, where a larger capacity teacher model with better quality is used to train
Knowledge Distillation (KD) is a common method for transferring the ``knowledge learned by one machine learning model (the textit{teacher}) into another model (the textit{student}), where typically, the teacher has a greater capacity (e.g., more para
We present Meta Learning for Knowledge Distillation (MetaDistil), a simple yet effective alternative to traditional knowledge distillation (KD) methods where the teacher model is fixed during training. We show the teacher network can learn to better
In most cases deep learning architectures are trained disregarding the amount of operations and energy consumption. However, some applications, like embedded systems, can be resource-constrained during inference. A popular approach to reduce the size
Generative Adversarial Networks (GAN) is an adversarial model, and it has been demonstrated to be effective for various generative tasks. However, GAN and its variants also suffer from many training problems, such as mode collapse and gradient vanish