Tensor networks (check this paper for a review) are a numerical method originally introduced in condensed matter physics to model complex quantum systems. Roughly speaking, such systems are described by a very high-dimensional tensor (where the indices take a number of values scaling exponentially with the number of system constituents) and tensor networks provide an efficient representation of the latter as an outer product and contraction of many low-dimensional tensors.
More recently, a specific kind of tensor network (called Matrix Product State in physics) found interesting applications in machine-learning through the so-called Tensor-Train decomposition (I do not know of a precise canonical reference in this context, so I will abstain from citing anything).
Now, over the last few years, several works from the physics community seemed to push for a generalized use of tensor networks in machine learning (see this paper, a second one and a third one and this article from Google AI for context). As a physicist, I am glad to learn that tools initially devised for physics may find interdisciplinary applications. However, at the same time, my critical mind tells me that from the machine learning research community's perspective, these results may not look that intriguing. After all, machine learning is now a very established field and it takes probably more than a suggestion for a new machine learning model and a basic benchmarking on a trivial dataset (as the MNIST one) -which is what the papers essentially do in my humble opinion- to attract any attention in the area. Besides, as I believe to know, there already exists quite a solid body of knowledge on tensor analysis techniques for machine learning (e.g. tensor decompositions), which may cast doubt on the originality of the contribution.
I would therefore be very curious to have the opinion of machine learning experts on this line of research: is it really an interesting direction to look into, or is it just about surfing on the current machine learning hype with a not-so-serious proposal?