  We propose a restricted class of tensor network state, built from
number-state preserving tensors, for supervised learning tasks. This class of
tensor network is argued to be a natural choice for classifiers as (i) they map
classical data to classical data, and thus preserve the interpretability of
data under tensor transformations, (ii) they can be efficiently trained to
maximize their scalar product against classical data sets, and (iii) they seem
to be as powerful as generic (unrestricted) tensor networks in this task. Our
proposal is demonstrated using a variety of benchmark classification problems,
where number-state preserving versions of commonly used networks (including
MPS, TTN and MERA) are trained as effective classifiers. This work opens the
path for powerful tensor network methods such as MERA, which were previously
computationally intractable as classifiers, to be employed for difficult tasks
such as image recognition.
