Differential geometry for Machine Learning

[kiuhnm]

My goal is to do research in Machine Learning (ML) and Reinforcement Learning (RL) in particular.
The problem with my field is that it's hugely multidisciplinary and it's not entirely clear what one should study on the mathematical side apart from multivariable calculus, linear algebra, probability, statistics and convex optimization.

Right now I'm interested in Information Geometry which is basically Differential Geometry with the Fisher metric. Here's a reference: https://metacademy.org/roadmaps/rgrosse/dgml
I'd like to know more about that topic, but to do that I need to first learn about Differential Geometry.
I think the author of that page underestimates the complexity of the task of learning all that in a useful way for doing research.

I watched the first 3 lectures of this course:

The teacher is great but the course is too shallow. I can understand all he says, but I miss my theorems and proofs. On the other hand I don't want to get John-M-Lee technical.

There's also another course by the same guy:

This one looks more in depth, but I still miss a book for the exercises and more examples.

What about the following book?
https://www.amazon.com/dp/0521829607/?tag=pfamazon01-20

Thank you for your time

 

[jedishrfu]

Here's a take on Discrete Differential Geometry which I find understandable.

https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf

It might give you what you need to understand Differential Geometry concepts.