Tensor Network Representation for Machine Learning: Theoretical Study and Algorithms Development

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We have developed several new tensor network decomposition and completion algorithms, and also developed the tensor network based neural network models and learning algorithms. These methods have been applied to several computer vision tasks.Specifically, we have developed tensorized RNN model that can achieve long term memory and reduced model size; we also studied Bayesian latent factor models to understand how tensor network is able to achieve model compression; our proposed tensor fusion layer can be applied to image denoting tasks with improvement performance, which can be also applied to the development of multimodal sentimental analysis. We also developed an efficient algorithm for classification on incomplete data samples, which has practical applications when the high-quality dataset is difficult to be obtained.From theoretical perspective, we have studied tensor nuclear norm and proposed several new definition of tensor norm, which has guarantee for exact recovery to tensor. In addition, we proposed a new type tensor network, called fully connected tensor network, which shows great flexibility on modeling complex interaction between tensor modes. The effectiveness of our theory and model is validated extensively on tensor completion tasks.