Revisiting Natural Gradient for Deep Networks
For researchers training deep networks, this work clarifies relationships between optimization methods and offers an enhanced natural gradient variant, though improvements are incremental.
The paper revisits natural gradient for deep networks, showing its connection to other methods and extending it to incorporate second-order information. Empirical results demonstrate improved robustness to training set ordering and better generalization when using unlabeled data.
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.