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Along with Prof. Samuel Kaski, I have been involved in helping PhD candidates get one of the highest university fellowships for graduate students - the Dean's Doctoral Scholarship. Hence maybe now I can say something about what is required to get this :)
IMHO, doing a Ph.D. is an extremely important decision in life and it can have significant ramifications on everything about oneself. Probably naturally, the Ph.D. admission is a very long and complex process and it's very important to start preparing the documents as early as possible. At our department, to have a chance at any of the important fellowships it is vitally important that the candidate has significant familiarity with their *intended* research field - just excellence in studies thus far is unlikely to cut it - I wrote a Ph.D. thesis on deep-learning while not knowing anything about neural nets till the middle of my first year of Ph.D. - unlikely this situation will fly here :D
So, to start a Ph.D. with me in the September of any year, ideally start having research discussions with me during the summer the year before ~ 1.5 years *before* the application deadline. I am assuming that at that point you already have demonstrable excellence in advanced maths/statistics/theoretical physics or E.C.E. courses - could be via top grades in these mathematically intensive courses. To maximize your chances, submit your applications (with the required TOEFL/IELTS scores) in December the year before - or definitely by March of the same year - though by then you would have already missed out on the chance to qualify for the President's Doctoral Scholar Award. This page lists all the funding possibilities that you can explore for doing your Ph.D. at our department.
(In particular, note if you qualify for any of the ``External Scholarships" listed therein.)
Almost Necessary Prerequisite Reading for Starting a PhD in Our Group
The students are expected to have evidence of understanding at least one or more of the following kinds of literature,
a)
Basics of stochastic optimization, like Chapter-6 here, https://arxiv.org/abs/1405.4980
b)
Basic machine learning theory, like these lectures, https://www.cs.princeton.edu/~rlivni/cos511/cos511.html
c)
Have top grades in any one of the topics, like PDE theory/advanced analysis/mathematical statistics/differential geometry/probability theory/Fourier analysis
and
have some familiarity with the lectures here,
https://youtube.com/playlist?list=PLJkYEExhe7rYY5HjpIJbgo-tDZ3bIAqAm&feature=shared
The lectures above are from a group in ETH Zurich with whom we have a close relationship.
Ideal Technical Background For Writing A Research Proposal in Deep-Learning (Theory)
It would be best, if a candidate would have not only had sufficient studies in topics mentioned above but also has research experience or courses done which have sufficient overlap with, say, these lecture notes by Matus Telgarsky or with the major themes covered in these reviews by Mikhail Belkin or the one by Peter Bartlett, Andrea Montanari and Sasha Rakhlin - or maybe most importantly have read at least parts of some of the canonical papers on the theory of operator learning like this one, https://doi.org/10.1093/imatrm/tnac001
Without the kind of background as evidenced in the references above - *irrespective* of one's previous depth of mathematical knowledge - it seems that to be able to put in a strong application it is almost crucial that we have had at least 2-3 months of weekly research discussions before the documents get submitted (either in December or in March). The expository notes linked above and the specific papers listed below are broadly indicative of the themes we could discuss.
Representative Deep-Learning Papers To Read Towards Joining Our Group
Feel free to pick your own path through these 6 papers.
I am arranging these references chronologically - but feel free to choose your own order of reading them.
It might be easier to read these papers, if alongside one is also reading any of the lecture notes or reviews mentioned above.
The themes in these papers are not identical,
- but these are representative of the kind of questions and directions that we want to think about!
https://arxiv.org/abs/1806.01796
https://arxiv.org/abs/1812.07956
https://arxiv.org/abs/2003.01897
https://arxiv.org/abs/2103.10974