2016/05/18 by E. Miles Stoudenmire, David J. Schwab · 2 voices · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #cond-mat.str-el #cs.LG #stat.ML
published as Advances in Neural Information Processing Systems 29, 4799 (2016) · 11 pages, 15 figures; updated version includes corrections, links to sample codes, expanded discussion, and additional references
arxiv published 2016/05/18 · arxiv created 2017/05/18 · arxiv updated 2017/05/22
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.