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arXiv · 1906.02353

Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks

Yi Ren·Donald Goldfarb
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Abstract

We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data sets. Our methods use subsampled Gauss-Newton or Fisher information matrices and either subsampled gradient estimates (fully stochastic) or full gradients (semi-stochastic), which, in the latter case, we prove convergent to a stationary point. By using the Sherman-Morrison-Woodbury formula with automatic differentiation (backpropagation) we show how our methods can be implemented to perform efficiently. Finally, numerical results are presented to demonstrate the effectiveness of our proposed methods.

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Yi Ren, Donald Goldfarb. 2019-06-05. Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks. https://arxiv.org/abs/1906.02353

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