Does the Data Induce Capacity Control in Deep Learning?. (arXiv:2110.14163v3 [cs.LG] UPDATED)

We show that the input correlation matrix of typical classification datasets
has an eigenspectrum where, after a sharp initial drop, a large number of small
eigenvalues are distributed uniformly over an exponentially large range. This
structure is mirrored in a network trained on this data: we show that the
Hessian and the Fisher Information Matrix (FIM) have eigenvalues that are
spread uniformly over exponentially large ranges. We call such eigenspectra
"sloppy" because sets of weights corresponding to small eigenvalues can …

arxiv capacity data deep learning learning lg