  Recently, deep neural networks (DNNs) have been regarded as the
state-of-the-art classification methods in a wide range of applications,
especially in image classification. Despite the success, the huge number of
parameters blocks its deployment to situations with light computing resources.
Researchers resort to the redundancy in the weights of DNNs and attempt to find
how fewer parameters can be chosen while preserving the accuracy at the same
time. Although several promising results have been shown along this research
line, most existing methods either fail to significantly compress a
well-trained deep network or require a heavy fine-tuning process for the
compressed network to regain the original performance. In this paper, we
propose the \textit{Block Term} networks (BT-nets) in which the commonly used
fully-connected layers (FC-layers) are replaced with block term layers
(BT-layers). In BT-layers, the inputs and the outputs are reshaped into two
low-dimensional high-order tensors, then block-term decomposition is applied as
tensor operators to connect them. We conduct extensive experiments on benchmark
datasets to demonstrate that BT-layers can achieve a very large compression
ratio on the number of parameters while preserving the representation power of
the original FC-layers as much as possible. Specifically, we can get a higher
performance while requiring fewer parameters compared with the tensor train
method.
