Latent Variable Models: Training LVM's using local search methods like EM, gradient descent, variational bayes etc. have a bunch of problems - they get stuck on local minima, the algorithms are hard to parallelize with poor convergence. In these cases, tensors yield guaranteed learning using embarassingly parallel algorithms, so faster convergence & can be run on Spark.
Also saw a demo on training 2-layer nets for GMM using tensors, and they learnt the weights rather fast. So using tensors in deep learning shows promise, though the techniques are in their infancy.
One of the challenges the professor mentioned was the availability of open source libraries to do tensor decomposition, which the above methods require.
It was a very successful talk - https://twitter.com/cdubhland/status/594220061025435649
Tensor slides: http://www.slideshare.net/SessionsEvents/animashree-anandkum...