Mirror descent of Hopfield model

Mirror descent is a gradient descent method that uses a dual space of parametric models. The great idea has been developed in convex optimization, but not yet widely applied in machine learning. In this study, we provide a possible way that the mirror descent can help data-driven parameter initialization of neural networks. We adopt the Hopfield model as a prototype of neural networks, we demonstrate that the mirror descent can train the model more effectively than the usual gradient descent with random parameter initialization.