After seeing this article https://www.quantamagazine.org/an-idea-from-physics-helps-ai-see-in-higher-dimensions-20200109/ I wanted to ask myself how useful of an endeavor would it be if one goes through the process of learning differential geometry to deep learning? Perhaps there are other tools as well?

Can concepts such as homotopy be 'appropriately' encodable in deep learning? I feel notions of homotopy invariance if properly defined could be much more valuable than the simple attempt in quantamagazine article. A basic attempt (away from deep learning framework) is in https://arxiv.org/abs/1408.2584.

eventuallybe a strong "yes, very useful". But as far as I am aware, at present it sounds like "maybe in some special cases" is more appropriate. $\endgroup$ – Ryan Budney Jan 11 at 20:37