AUTHOR=Liu Yuhan , Li Wen-Jun , Zhang Xiao , Lewenstein Maciej , Su Gang , Ran Shi-Ju TITLE=Entanglement-Based Feature Extraction by Tensor Network Machine Learning JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=7 YEAR=2021 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.716044 DOI=10.3389/fams.2021.716044 ISSN=2297-4687 ABSTRACT=

It is a hot topic how entanglement, a quantity from quantum information theory, can assist machine learning. In this work, we implement numerical experiments to classify patterns/images by representing the classifiers as matrix product states (MPS). We show how entanglement can interpret machine learning by characterizing the importance of data and propose a feature extraction algorithm. We show on the MNIST dataset that when reducing the number of the retained pixels to 1/10 of the original number, the decrease of the ten-class testing accuracy is only O (10–3), which significantly improves the efficiency of the MPS machine learning. Our work improves machine learning’s interpretability and efficiency under the MPS representation by using the properties of MPS representing entanglement.