Supervised Learning with Projected Entangled Pair States

TL;DR

This paper introduces a novel supervised learning model for image classification using projected entangled pair states (PEPS), a 2D tensor network, demonstrating superior performance over tree-like tensor networks and comparable results to multilayer perceptrons with fewer parameters.

Contribution

The paper presents the first application of PEPS, a 2D tensor network, for supervised image classification, showing improved accuracy and efficiency over existing tensor network models.

Findings

PEPS-based model outperforms tree tensor network models on MNIST datasets.

The model achieves comparable accuracy to multilayer perceptrons with fewer parameters.

The approach is more stable and efficient than existing tensor network models.

Abstract

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as the matrix product states and tree tensor networks have been considered, even for modeling two-dimensional data such as images. In this work, we construct supervised learning models for images using the projected entangled pair states (PEPS), a two-dimensional tensor network having a similar structure prior to natural images. Our approach first performs a feature map, which transforms the image data to a product state on a grid, then contracts the product state to a PEPS with trainable parameters to predict image labels. The tensor elements of PEPS are trained by minimizing differences between training labels and predicted labels. The proposed model is evaluated on image classifications using the MNIST and the Fashion-MNIST datasets. We show that our model is significantly superior to existing models using tree-like tensor networks. Moreover, using the same input features, our method performs as well as the multilayer perceptron classifier, but with much fewer parameters and is more stable. Our results shed light on potential applications of two-dimensional tensor network models in machine learning.