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I am partway through my PhD studying deep learning. I chose it just because it's useful and would yield a lot of industry opportunities. However, I am really missing my previous coursework in computability theory and complexity theory. I would like to get involved in this area of math/cs. Does anyone know how I can do so? Should I just finish my PhD and do a postdoc? Are there many postdocs available for math logic/cs theory and would they take someone who studied AI with no research experience in that area?

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    $\begingroup$ That would depend a lot on where you are doing your PhD (currently), and whether there are any faculty there working on computability and complexity theory — you may want to provide these details. $\endgroup$
    – Clement C.
    Mar 25, 2022 at 11:13
  • $\begingroup$ @ClementC. Yeah so a big issue is that there's no faculty doing that in my university right now. It's also not ranked very high. Do you think I could jump somewhere else to study this? $\endgroup$ Mar 25, 2022 at 16:15
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    $\begingroup$ The first thing that comes to mind is: have you talked to your PhD advisor(s)? What do they say/suggest? Unless there is a good reason not to ask them, they would be much better placed (given available info, etc.) to provide you valuable advice than us. $\endgroup$
    – Clement C.
    Mar 26, 2022 at 10:03
  • $\begingroup$ As a first step, I would recommend aiming at building some bridges between the areas. Identify a problem in deep learning that has open complexity status, and try to resolve it. Try to find reductions between deep learning tasks. Or try to prove some upper/lower bounds on running times for deep learning algorithms. Try to investigate what happens if you allow using oracles in deep learning algorithms. Which algorithm can gain a speed-up? How much is the speed-up, which oracles can provide it, and how? Such results can place you on the borderline and then allow moving into either area. $\endgroup$ Mar 28, 2022 at 2:51

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