Natural Gradient Descent

Natural gradient descent (NGD) is a second-order optimization method that improves upon standard gradient descent by incorporating information about the curvature of the loss landscape, leading to faster convergence and potentially better generalization. Current research focuses on developing efficient approximations of the computationally expensive Fisher Information Matrix (FIM) used in NGD, particularly for deep learning models, with approaches like Kronecker-factored approximations and inverse-free methods gaining traction. These advancements are significant because they make NGD more practical for large-scale applications, impacting fields like machine learning, reinforcement learning, and scientific computing where efficient optimization is crucial.