  We evaluate natural gradient, an algorithm originally proposed in Amari
(1997), for learning deep models. The contributions of this paper are as
follows. We show the connection between natural gradient and three other
recently proposed methods for training deep models: Hessian-Free (Martens,
2010), Krylov Subspace Descent (Vinyals and Povey, 2012) and TONGA (Le Roux et
al., 2008). We describe how one can use unlabeled data to improve the
generalization error obtained by natural gradient and empirically evaluate the
robustness of the algorithm to the ordering of the training set compared to
stochastic gradient descent. Finally we extend natural gradient to incorporate
second order information alongside the manifold information and provide a
benchmark of the new algorithm using a truncated Newton approach for inverting
the metric matrix instead of using a diagonal approximation of it.
