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arXiv · 1910.12194

A geometric interpretation of stochastic gradient descent using diffusion metrics

R. Fioresi·P. Chaudhari·S. Soatto
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Abstract

Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are described via geodesics of a family of metrics arising from the diffusion matrix. These metrics encode information about the highly non-isotropic gradient noise in SGD. We establish a parallel with General Relativity models, where the role of the electromagnetic field is played by the gradient of the loss function. We compute an example of a two layer network.

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R. Fioresi, P. Chaudhari, S. Soatto. 2019-10-27. A geometric interpretation of stochastic gradient descent using diffusion metrics. https://doi.org/10.3390/e22010101

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