  Tensor decomposition is an effective approach to compress over-parameterized
neural networks and to enable their deployment on resource-constrained hardware
platforms. However, directly applying tensor compression in the training
process is a challenging task due to the difficulty of choosing a proper tensor
rank. In order to achieve this goal, this paper proposes a Bayesian tensorized
neural network. Our Bayesian method performs automatic model compression via an
adaptive tensor rank determination. We also present approaches for posterior
density calculation and maximum a posteriori (MAP) estimation for the
end-to-end training of our tensorized neural network. We provide experimental
validation on a fully connected neural network, a CNN and a residual neural
network where our work produces $7.4\times$ to $137\times$ more compact neural
networks directly from the training.
