Deep learning, stochastic gradient descent and diffusion maps. (arXiv:2204.01365v3 [stat.ML] UPDATED)

Web: http://arxiv.org/abs/2204.01365

Stochastic gradient descent (SGD) is widely used in deep learning due to its
computational efficiency, but a complete understanding of why SGD performs so
well remains a major challenge. It has been observed empirically that most
eigenvalues of the Hessian of the loss functions on the loss landscape of
over-parametrized deep neural networks are close to zero, while only a small
number of eigenvalues are large. Zero eigenvalues indicate zero diffusion along
the corresponding directions. This indicates that the process …

arxiv deep deep learning gradient learning maps ml stochastic