Uncover Hidden Low-Rank Tensors in Noisy Data with Machine Learning 🔍

Someone gives you a tensor. You have a hunch that it is a noisy observation of an underlying tensor which is low rank. Depending on what kind of noise has been applied, can you recover the underlying matrix, at least approximately? Can you do this efficiently? And how much noise can you tolerate? And what does this have to do with statistical physics?