  The tensor network, as a facterization of tensors, aims at performing the
operations that are common for normal tensors, such as addition, contraction
and stacking. However, due to its non-unique network structure, only the tensor
network contraction is so far well defined. In this paper, we propose a
mathematically rigorous definition for the tensor network stack approach, that
compress a large amount of tensor networks into a single one without changing
their structures and configurations. We illustrate the main ideas with the
matrix product states based machine learning as an example. Our results are
compared with the for loop and the efficient coding method on both CPU and GPU.
