I can only speak from experience in my CS PhD program, but my above recommendations are based directly on that experience. We have an exam after the first two

I can only speak from experience in my CS PhD program, but my above recommendations are based directly on that experience. We have an exam after the first two years and a similar process. It depends on what your advisor expects/wants. Mine has been flexible. And I focused more on efficient software engineering and applications for prior methods than on new research as I got up to speed on other matters. It made obvious a lot of ways I could improve them, just by being forced to look at and implement all of the details under the hood. And, at least in my CS department, there is a very heavy emphasis on mathematics with the ML/AI folks. They coauthor a number of papers with the applied math department and the rest of their papers are mostly proofs. They'll usually back it up with proof-of-concept implementations, but in that regard, they're very much like researchers in applied math except that they use Python instead of MATLAB.