Learning using the Born Rule

Abstract

In Quantum Mechanics the transition from a deterministic descriptionto a probabilistic one is done using a simple rule termed the Bornrule. This rule states that the probability of an outcome ($a$)given a state ($\Psi$) is the square of their inner products($(a^\top\Psi)^2$).In this paper, we unravel a new probabilistic justification forpopular algebraic algorithms, based on the Born rule. Thesealgorithms include two-class and multiple-class spectral clustering,and algorithms based on Euclidean distances.