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We apply state-of-the-art tools in modern high-dimensional numerical linearalgebra to approximate efficiently the spectrum of the Hessian of moderndeepnets, with tens of millions of parameters, trained on real data. Ourresults corroborate previous findings, based on small-scale networks, that theHessian exhibits "spiked" behavior, with several outliers isolated from acontinuous bulk. We decompose the Hessian into different components and studythe dynamics with training and sample size of each term individually.

The Full Spectrum of Deepnet Hessians at Scale: Dynamics with SGD Training and Sample Size