Before revision:  Therefore, we propose a general mathematical framework to study inference with iteratively applied perturbations to a network. 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:  Therefore, we propose a general mathematical framework to study inference with iteratively applied perturbations . Using the formulation 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.