[D] Seeking perspectives from PhDs in math regarding ML research.

About me: Finishing a PhD in Math (specializing in geometry and gauge theory) with a growing interest in the theoretical foundations and applications of ML. I had some questions for Math PhDs who transitioned to doing ML research.

1. Which textbooks or seminal papers offer the most “mathematically satisfying” treatment of ML? Which resources best bridge the gap between abstract theory and the heuristics of modern ML research?
2. How did your specific mathematical background influence your perspective on the field? Did your specific doctoral sub-field already have established links to ML?

Field Specific

1. Aside from the standard E(n)-equivariant networks and GDL frameworks, what are the most non-trivial applications of geometry in ML today?
2. Is the use of stochastic calculus on manifolds in ML deep and structural (e.g., in diffusion models or optimization), or is it currently applied in a more rudimentary fashion?
3. Between the different degrees of rigidity in geometry (topological, differential, algebraic, and symplectic geometry etc.) which sub-field currently hosts the most active and rigorous intersections with ML research?