# Number-State Preserving Tensor Networks as Classifiers for Supervised Learning

arXiv: https://arxiv.org/abs/1905.06352 · HTML: https://mlsanity.com/paper/1905.06352/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 3 of 3)

- [Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification](https://mlsanity.com/paper/2101.03154/) (2021)
- [Differentiable Programming of Isometric Tensor Networks](https://mlsanity.com/paper/2110.03898/) (2021)
- [Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks](https://mlsanity.com/paper/2504.14995/) (2025)

## Abstract (arXiv)

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.