  This work focuses on designing low complexity hybrid tensor networks by
considering trade-offs between the model complexity and practical performance.
Firstly, we exploit a low-rank tensor-train deep neural network (TT-DNN) to
build an end-to-end deep learning pipeline, namely LR-TT-DNN. Secondly, a
hybrid model combining LR-TT-DNN with a convolutional neural network (CNN),
which is denoted as CNN+(LR-TT-DNN), is set up to boost the performance.
Instead of randomly assigning large TT-ranks for TT-DNN, we leverage Riemannian
gradient descent to determine a TT-DNN associated with small TT-ranks.
Furthermore, CNN+(LR-TT-DNN) consists of convolutional layers at the bottom for
feature extraction and several TT layers at the top to solve regression and
classification problems. We separately assess the LR-TT-DNN and CNN+(LR-TT-DNN)
models on speech enhancement and spoken command recognition tasks. Our
empirical evidence demonstrates that the LR-TT-DNN and CNN+(LR-TT-DNN) models
with fewer model parameters can outperform the TT-DNN and CNN+(TT-DNN)
counterparts.
