The Full Spectrum of Deep Net Hessians At Scale: Dynamics with Sample Size
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Previous works observed the spectrum of the Hessian of the training loss of deep neural networks. However, the networks considered were of minuscule size. We apply state-of-the-art tools in modern high-dimensional numerical linear algebra to approximate the spectrum of the Hessian of deep nets with tens of millions of parameters. Our results corroborate previous findings, based on small-scale networks, that the Hessian exhibits 'spiked' behavior, with several outliers isolated from a continuous bulk. However we find that the bulk does not follow a simple Marchenko-Pastur distribution, as previously suggested, but rather a heavier-tailed distribution. Finally, we document the dynamics of the outliers and the bulk with varying sample size.
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