  Natural gradient descent is a principled method for adapting the parameters
of a statistical model on-line using an underlying Riemannian parameter space
to redefine the direction of steepest descent. The algorithm is examined via
methods of statistical physics which accurately characterize both transient and
asymptotic behavior. A solution of the learning dynamics is obtained for the
case of multilayer neural network training in the limit of large input
dimension. We find that natural gradient learning leads to optimal asymptotic
performance and outperforms gradient descent in the transient, significantly
shortening or even removing plateaus in the transient generalization
performance which typically hamper gradient descent training.
