In some sense DG is the foundation of all modern AI/ML/DL approach. The bar is just too high for normal people
in what sense? i love when people say pretentious things like this to sound authoritative.
just because you take derivatives doesn't mean it's calculus. DG is not calculus - DG is calculus in spaces aren't globally flat but are locally flat. very different.
>The bar is just too high for normal people
in most schools that have DG classes they're junior level. certainly this class is a junior level class
http://brickisland.net/DDGSpring2019/grading-policy/
(no i didn't attend CMU or any similar tier school so i'm not speaking from a place of dunning-Kruger)
>It would indeed be interesting to see a coherent description of ML in a DG framework.
there is no need for such a thing - you don't need the machinery of connections, bundles, christoffel symbols, whatever else in order to take derivatives. you use those tools to be able to take derivatives in places where you can't do freshman calculus, not the other way around (bring those tools to places where you do do freshman calculus). it makes no sense.
it's like reasoning that because wiles used algebraic geometry to resolve fermat's last theorem that solving quadratic equations is really about algebraic geometry.
There are quite a few places differential geometry is very useful to know. Generally, if you want to know at a fundamental level "what does it mean to learn, what is inference truly?". You will find yourself in dire need of learning differential geometry. The easiest example is: the deeper your understanding of differential geometry, the more you'll be able to reason about hamiltonian monte carlo algorithms.
Information geometry also applies differential geometry, where you can think of learning as trajectories on a statistical manifold.
K-FAC, mirror descent and the natural gradient also derive from or are closely connected to work in information geometry. There's recent work connecting optimal transport. Optimal transport is an important idea and pops up in many surprising places, from GANs to programming language theory via way of modeling concurrency, for example (Kantorovich metric for bisimulation). Understanding differential geometry allows you to see and navigate such rich connections at a deep level. I heartily recommend it. A good place to start is: https://metacademy.org/roadmaps/rgrosse/dgml
https://arxiv.org/pdf/1410.3831v1.pdf
that's occupies very rarefied air, but that's not what the person to whom i'm responding to claims (that somewhere someone there's a relationship):
>DG is the foundation of all modern AI/ML/DL
which is just blather spoken in a tone of confidence in order to sound very smart.