  Deep neural networks have achieved a great success in solving many machine
learning and computer vision problems. The main contribution of this paper is
to develop a deep network based on Tucker tensor decomposition, and analyze its
expressive power. It is shown that the expressiveness of Tucker network is more
powerful than that of shallow network. In general, it is required to use an
exponential number of nodes in a shallow network in order to represent a Tucker
network. Experimental results are also given to compare the performance of the
proposed Tucker network with hierarchical tensor network and shallow network,
and demonstrate the usefulness of Tucker network in image classification
problems.
