论文标题
一维张量网络恢复
One-dimensional Tensor Network Recovery
论文作者
论文摘要
我们研究了张量环或张量火车格式中张量的基础图或置换量的恢复。我们提出的算法比较了在下采样后的入学排名，其复杂性为$ O（d \ log d）$，对于$ d $ th的订单张量。我们证明，当可以在没有噪声的情况下观察张量的条目时，我们的算法几乎可以肯定地恢复正确的图形或排列。我们进一步建立了算法对观察噪声的鲁棒性。理论结果通过数值实验验证。
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 $O(d\log d)$ for $d$-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.
