Description: Deep learning has been reported to improve upon previous state of the art in many traditional machine learning tasks, like image classification, recommender systems, text-to-speech, and so on. Nevertheless, there are still fundamentally problematic issues with these systems, that invite theoretical work on extensions of deep learning towards (traditional) probabilistic reasoning. This is a topic of some interest, which has lead to nice tools that can be used for implementation/evaluation, like Tensorflow Probability and Pyro (built on top of PyTorch). For typical research trends, see Part III of "The Deep Learning Book" by Goodfellow et al. The selection of interesting research question(s) in this area will depend on the students' interest.
Level of sophistication: This is a difficult yet rewarding topic to work on. Students taking on this challenge should expect to do more demanding work than your run-of-the-mill project/master thesis. A good grasp of linear algebra, standard statistics, general machine learning, and deep learning is required for this to be fun. Furthermore, you will be expected to implement the ideas you develop in a deep learning framework, hence you will need to learn how to find your way around in Tensorflow, PyTorch, or similar, too.
Finally, please look at this link for the procedure to sign up for the project: www.idi.ntnu.no/~helgel/teaching/proposals/