Entanglement-Based Feature Extraction by Tensor Network Machine Learning - Liu, Yuhan; Li, Wen-Jun; Zhang, Xiao; Lewenstein, Maciej; Su, Gang; Ran, Shi-Ju (Frontiers in Applied Mathematics and Statistics, 2021)
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.