Supervised Learning with Quantum-Inspired Tensor Networks
This work introduces a novel method for machine learning practitioners, though it is incremental as it adapts existing tensor network techniques to a new domain.
The authors tackled the problem of applying tensor networks to supervised learning by adapting matrix product states for image classification, achieving less than 1% test error on MNIST.
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.