  The paper surveys the topic of tensor decompositions in modern machine
learning applications. It focuses on three active research topics of
significant relevance for the community. After a brief review of consolidated
works on multi-way data analysis, we consider the use of tensor decompositions
in compressing the parameter space of deep learning models. Lastly, we discuss
how tensor methods can be leveraged to yield richer adaptive representations of
complex data, including structured information. The paper concludes with a
discussion on interesting open research challenges.
