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Deep neural networks can suffer from the exploding and vanishing activation problem, in which the networks fail to train properly because the neural signals either amplify or attenuate across the layers and become saturated. While other normalization methods aim to fix the stated problem, most of them have inference speed penalties in those applications that require running averages of the neural activations. Here we extend the unitary framework based on Lie algebra to neural networks of any dimensionalities, overcoming the major constraints of the prior arts that limit synaptic weights to be square matrices. Our proposed unitary convolutional neural networks deliver up to 32% faster inference speeds and up to 50% reduction in permanent hard disk space while maintaining competitive prediction accuracy.
Deep convolutional neural networks (CNNs) have been actively adopted in the field of music information retrieval, e.g. genre classification, mood detection, and chord recognition. However, the process of learning and prediction is little understood,
Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we propose Param
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and ed
Convolutional Neural Networks (CNN) have redefined the state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to