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Deep neural networks have achieved great success in solving many machine learning and computer vision problems. In this paper, we propose a deep neural network called the Tucker network derived from the Tucker format and analyze its expressive power. The results demonstrate that the Tucker network has exponentially higher expressive power than the shallow network. In other words, a shallow network with an exponential width is required to realize the same score function as that computed by the Tucker network. Moreover, we discuss the expressive power between the hierarchical Tucker tensor network (HT network) and the proposed Tucker network. To generalize the Tucker network into a deep version, we combine the hierarchical Tucker format and Tucker format to propose a deep Tucker tensor decomposition. Its corresponding deep Tucker network is presented. Experiments are conducted on three datasets: MNIST, CIFAR-10 and CIFAR-100. The results experimentally validate the theoretical results and show that the Tucker network and deep Tucker network have better performance than the shallow network and HT network. [ABSTRACT FROM AUTHOR]

Fully connected deep neural networks (DNN) often include redundant weights leading to overfitting and high memory requirements. Additionally, in tabular data classification, DNNs are challenged by the often superior performance of traditional machine learning models. This paper proposes periodic perturbations (prune and regrow) of DNN weights, especially at the self-supervised pre-training stage of deep autoencoders. The proposed weight perturbation strategy outperforms dropout learning or weight regularization (L1 or L2) for four out of six tabular data sets in downstream classification tasks. Unlike dropout learning, the proposed weight perturbation routine additionally achieves 15% to 40% sparsity across six tabular data sets, resulting in compressed pretrained models. The proposed pretrained model compression improves the accuracy of downstream classification, unlike traditional weight pruning methods that trade off performance for model compression. Our experiments reveal that a pretrained deep autoencoder with weight perturbation can outperform traditional machine learning in tabular data classification, whereas baseline fully-connected DNNs yield the worst classification accuracy. However, traditional machine learning models are superior to any deep model when a tabular data set contains uncorrelated variables. Therefore, the performance of deep models with tabular data is contingent on the types and statistics of constituent variables. [ABSTRACT FROM AUTHOR]