The paper proposes a tensorized variation on restricted Boltzmann machines (RBMs) to reduce the number of model parameters and significantly decrease training time, while still obtaining comparable performance. The approach is demonstrated on three applications: face reconstruction, handwritten digit recognition, and image super-resolution.

Some of the experimental results are good--better than with other similar methods--but they seem to be parameter dependent. The paper is highly technical and detailed, but it does not give any indication as to how a user should select the parameters. A discussion on how to choose the parameters would have been a valuable addition.

I would also have liked to see a broad discussion comparing RBMs with generative adversarial networks or with variational autoencoders, to put the contribution in the current context where RBMs seem somehow to be out of fashion.

There are a lot of acronyms in the paper. Some acronyms are well known, such as peak signal-to-noise ratio (PSNR), but it would have been helpful to expand them. The paper is understandable, but the writing is not as polished as one would expect of a high-quality journal.