Reviews: Singleshot : a scalable Tucker tensor decomposition

The paper proposes efficient methods for computing the Tucker decomposition of higher-order tensors. The problem is a hard, basic problem in numerical linear algebra with reasonably wide applicability. Tensor decompositions have played an important role in a variety of machine learning applications, see for example: Anandkumar et al "Tensor Decompositions for Learning Latent Variable Models" JMLR 2014; Novikov et al "Tensorizing Neural Networks" NeurIPS 2015, which used tensor decompositions to massively compress the dense layers of VGG; Moitra and Wein "Spectral Methods from Tensor Networks"; and Becker and Osman "Low rank Tucker decompositions of large tensors using tensorsketch" NeurIPS 2018. Singleshot is a coordinate descent based algorithm which applies gradient updates to variables in the Tucker decomposition, which it cycles over. The paper carefully considers the memory usage of Singleshot (and its variants) since tensor computations are often extremely memory intensive.