The Underlying Scaling Laws and Universal Statistical Structure of Complex Datasets

arXiv:2306.14975v3 Announce Type: replace
Abstract: We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory (RMT) to reveal their underlying structure. We focus on the feature-feature covariance matrix, analyzing both its local and global eigenvalue statistics. Our main observations are: (i) The power-law scalings that the bulk of its eigenvalues exhibit are …

abstract arxiv cond-mat.dis-nn cs.lg data datasets generated hep-th laws math.pr matrix physics random scaling statistical stat.ml study theory tools type universal world