In my mind the trick is always in training models as it amounts to picking an optimal probability distribution from your manifold. Even in relatively simple mat

In my mind the trick is always in training models as it amounts to picking an optimal probability distribution from your manifold. Even in relatively simple mathematical statistics we quickly encounter curvature in exponential families but the tools to handle it are ad hoc. Differential geometry provides exactly the right tools to both talk about curvature and to talk about traversing the manifold and that is an appropriate place to talk about maximization as is needed. https://projecteuclid.org/euclid.aos/1176345779 https://projecteuclid.org/euclid.aos/1176345779