A tensor network is a type of decomposition used to express and approximate
large arrays of data. A given data-set, quantum state or higher dimensional
multi-linear map is factored and approximated by a composition of smaller
multi-linear maps. This is reminiscent to how a Boolean function might be
decomposed into a gate array: this represents a special case of tensor
decomposition, in which the tensor entries are replaced by 0, 1 and the
factorisation becomes exact. The collection of associated techniques are
called, tensor network methods: the subject developed independently in several
distinct fields of study, which have more recently become interrelated through
the language of tensor networks. The tantamount questions in the field relate
to expressability of tensor networks and the reduction of computational
overheads. A merger of tensor networks with machine learning is natural. On the
one hand, machine learning can aid in determining a factorization of a tensor
network approximating a data set. On the other hand, a given tensor network
structure can be viewed as a machine learning model. Herein the tensor network
parameters are adjusted to learn or classify a data-set. In this survey we
recover the basics of tensor networks and explain the ongoing effort to develop
the theory of tensor networks in machine learning.

这篇论文介绍了张量网络及其在机器学习中的应用，张量网络通过分解大规模数据矩阵来实现数据的近似表达与计算的降维，是一种常用的数据处理技术。