Unlock: Fisher Information: Curvature, KL Geometry, and the Natural Gradient

The Fisher information measures how much a sample tells you about an unknown parameter. Coverage of the score function and Bartlett identities, the equivalence of variance-of-score and expected-negative-Hessian forms, the KL-divergence Hessian identity, the Fisher information matrix and Loewner ordering, the Cramér-Rao link, the natural gradient (parameterization invariance), K-FAC and empirical Fisher in deep learning, and applications to MLE asymptotic efficiency, EWC, and information geometry.