[vjktyu]

Study calculus, from the definition of real numbers and to taking complex integrals via residuals; then study linear algebra to some theorems about eigenvectors. 1 month total, assuming you're somewhat talented and determined to spend 12 hours a day learning proofs of boring theorems. After that you'll realise that most of the ML papers out there are just ad-hoc composed matrix multiplications with some formulas used as fillers. At that point I think it's more useful to learn what ML models work in practice (although nobody will be able to explain why they work, including the authors) and mix this practical knowledge with the math theory to develop good intuition.

I'd compare ML with weather models: we understand physics driving individual particles, we understand the high level diff equations, but as complexity builds up, we have to resort to intuition to develop at least somewhat working weather models.

[mkl]

What are complex integrals used for in machine learning?

[vjktyu]

They aren't. It's just a very coarse point where to stop.