Number-State Preserving Tensor Networks as Classifiers for Supervised Learning
This work enables computationally intractable tensor network methods like MERA to be applied to difficult tasks such as image recognition, representing an incremental advancement for the machine learning community.
The authors tackled the problem of using tensor networks for supervised learning by proposing a restricted class of number-state preserving tensors as classifiers, demonstrating their effectiveness on benchmark classification tasks with results comparable to generic tensor networks.
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.