One-Dimensional Tensor Network Recovery

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1217-1244, September 2024.
Abstract. We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is [math] for [math]th-order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.