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arXiv · 1808.10340

A Coordinate-Free Construction of Scalable Natural Gradient

Kevin Luk·Roger Grosse
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Abstract

Most neural networks are trained using first-order optimization methods, which are sensitive to the parameterization of the model. Natural gradient descent is invariant to smooth reparameterizations because it is defined in a coordinate-free way, but tractable approximations are typically defined in terms of coordinate systems, and hence may lose the invariance properties. We analyze the invariance properties of the Kronecker-Factored Approximate Curvature (K-FAC) algorithm by constructing the algorithm in a coordinate-free way. We explicitly construct a Riemannian metric under which the natural gradient matches the K-FAC update; invariance to affine transformations of the activations follows immediately. We extend our framework to analyze the invariance properties of K-FAC applied to convolutional networks and recurrent neural networks, as well as metrics other than the usual Fisher metric.

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Kevin Luk, Roger Grosse. 2018-08-30. A Coordinate-Free Construction of Scalable Natural Gradient. https://arxiv.org/abs/1808.10340

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