Learning functions on symmetric matrices and point clouds via lightweight invariant features

arXiv:2405.08097v1 Announce Type: new
Abstract: In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are invariant with respect to rotations, reflections, and permutations of the points. To achieve this, we construct $O(n^2)$ invariant features derived from generators for the field of rational functions on $n\times n$ symmetric matrices that are invariant under joint …

abstract arxiv cs.lg features functions machine machine learning permutations reflections type via work