Before revision:  Formulating active learning in the language of information geometry, our framework quantifies the difficulty of inference as well as the information gain due to perturbations through the curvature of the underlying parameter manifold as measured though the empirical Fisher information.
After revision:  Formulating active learning in the language of information geometry, our framework quantifies the difficulty of inference as well as the information gain due to perturbations through the curvature of the underlying parameter manifold , measured by Fisher information.