The most intriguing use cases I've seen is for when it gets used to create better estimators (using the geometry of the Fisher information matrix). I guess it w

The most intriguing use cases I've seen is for when it gets used to create better estimators (using the geometry of the Fisher information matrix). I guess it works particularly well on things like the EM algorithm, but there are probably lots of signal processing-ey applications. People babbling about neural nets; that's probably wrong -never seen an actual application there, though TDA does very interesting things for neural approaches for reasons that should be obvious. I kind of wish I had done the GR course with Carlo Rovelli and Ezra Newman back when I had the chance; the first semester was all differential geometry, and those dudes were great at explaining math. Since the Einstein equations are more nasty than the Fisher information matrix, it would have made all the info-geo stuff pretty accessible.