  The existing tensor networks adopt conventional matrix product for
connection. The classical matrix product requires strict dimensionality
consistency between factors, which can result in redundancy in data
representation. In this paper, the semi-tensor product is used to generalize
classical matrix product-based mode product to semi-tensor mode product. As it
permits the connection of two factors with different dimensionality, more
flexible and compact tensor decompositions can be obtained with smaller sizes
of factors. Tucker decomposition, Tensor Train (TT) and Tensor Ring (TR) are
common decomposition for low rank compression of deep neural networks. The
semi-tensor product is applied to these tensor decompositions to obtained their
generalized versions, i.e., semi-tensor Tucker decomposition (STTu),
semi-tensor train(STT) and semi-tensor ring (STR). Experimental results show
the STTu, STT and STR achieve higher compression factors than the conventional
tensor decompositions with the same accuracy but less training times in ResNet
and WideResNetcompression. With 2% accuracy degradation, the TT-RN (rank = 14)
and the TR-WRN (rank = 16) only obtain 3 times and99t times compression factors
while the STT-RN (rank = 14) and the STR-WRN (rank = 16) achieve 9 times and
179 times compression factors, respectively.
