I have seen Riemann geometry applied to neural networks. Basically the state space is curved, so you can speed up learning if take the curvature into account wh

I have seen Riemann geometry applied to neural networks. Basically the state space is curved, so you can speed up learning if take the curvature into account when sampling in the space of possible neural nets. (you want to explore the hypothesis space evenly) Information geometry for Neural networks, 1998, Daniel Wagenaar:- http://www.danielwagenaar.net/res/papers/98-Wage2.pdf http://www.danielwagenaar.net/res/papers/98-Wage2.pdf