Directional Analysis of Stochastic Gradient Descent via von Mises-Fisher Distributions in Deep Learning

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dc.contributor.authorLee, Cheolhyungko
dc.contributor.authorCho, Kyunghyunko
dc.contributor.authorKang, Wanmoko
dc.identifier.citationThirty-second Conference on Neural Information Processing Systems-
dc.description.abstractAlthough stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better characterize the learning dynamics of SGD. Inspired from these work, we here analyze SGD from a geometrical perspective by inspecting the stochasticity of the norms and directions of minibatch gradients. We propose a model of the directional concentration for minibatch gradients through von Mises-Fisher (VMF) distribution, and show that the directional uniformity of minibatch gradients increases over the course of SGD. We empirically verify our result using deep convolutional networks and observe a higher correlation between the gradient stochasticity and the proposed directional uniformity than that against the gradient norm stochasticity, suggesting that the directional statistics of minibatch gradients is a major factor behind SGD.-
dc.publisherNeural Information Processing Systems (NIPS) Foundation-
dc.titleDirectional Analysis of Stochastic Gradient Descent via von Mises-Fisher Distributions in Deep Learning-
dc.citation.publicationnameThirty-second Conference on Neural Information Processing Systems-
dc.identifier.conferencelocationMontreal Convention Center-
dc.contributor.localauthorKang, Wanmo-
dc.contributor.nonIdAuthorCho, Kyunghyun-
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MA-Conference Papers(학술회의논문)
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