Neural learning by retractions on manifolds

Neural learning algorithms based on criterion optimization over differential manifolds have been devised over the few past years. Such learning algorithms mainly differ by the way the single learning steps are effected on the neural system's parameter space. We introduce a unifying view of these algorithms by recalling from the literature of differential geometry the concept of retraction on manifolds. It provides a general way of acting upon neural system's learnable parameters for learning criteria optimization purpose. © 2007 IEEE.