Supervised Learning with Quantum-Inspired Tensor Networks

TL;DR

This paper explores how tensor networks, specifically matrix product states, can be adapted for supervised learning, achieving high accuracy on image classification tasks like MNIST, and discusses their structural and generative properties.

Contribution

It introduces a novel application of tensor networks to supervised learning, demonstrating effective image classification with less than 1% error on MNIST.

Findings

Achieved less than 1% test error on MNIST

Adapted tensor network algorithms for supervised learning

Discussed structural and generative aspects of the models

Abstract

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models for classifying images. For the MNIST data set we obtain less than 1% test set classification error. We discuss how the tensor network form imparts additional structure to the learned model and suggest a possible generative interpretation.