On the Power-Law Hessian Spectrums in Deep Learning. (arXiv:2201.13011v2 [cs.LG] UPDATED)

It is well-known that the Hessian of deep loss landscape matters to
optimization, generalization, and even robustness of deep learning. Recent
works empirically discovered that the Hessian spectrum in deep learning has a
two-component structure that consists of a small number of large eigenvalues
and a large number of nearly-zero eigenvalues. However, the theoretical
mechanism or the mathematical behind the Hessian spectrum is still largely
under-explored. To the best of our knowledge, we are the first to demonstrate
that the …

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