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We propose a restricted class of tensor network state, built fromnumber-state preserving tensors, for supervised learning tasks. This class oftensor network is argued to be a natural choice for classifiers as (i) they mapclassical data to classical data, and thus preserve the interpretability ofdata under tensor transformations, (ii) they can be efficiently trained tomaximize their scalar product against classical data sets, and (iii) they seemto be as powerful as generic (unrestricted) tensor networks in this task. Ourproposal is demonstrated using a variety of benchmark classification problems,where number-state preserving versions of commonly used networks (includingMPS, TTN and MERA) are trained as effective classifiers. This work opens thepath for powerful tensor network methods such as MERA, which were previouslycomputationally intractable as classifiers, to be employed for difficult taskssuch as image recognition.

Number-State Preserving Tensor Networks as Classifiers for Supervised Learning