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arXiv · 1812.04754

Gradient Descent Happens in a Tiny Subspace

Guy Gur-Ari·Daniel A. Roberts·Ethan Dyer
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Abstract

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of training. A simple argument then suggests that gradient descent may happen mostly in this subspace. We give an example of this effect in a solvable model of classification, and we comment on possible implications for optimization and learning.

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Guy Gur-Ari, Daniel A. Roberts, Ethan Dyer. 2018-12-12. Gradient Descent Happens in a Tiny Subspace. https://arxiv.org/abs/1812.04754

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