Laplace-HDC: Understanding the geometry of binary hyperdimensional computing

arXiv:2404.10759v1 Announce Type: new
Abstract: This paper studies the geometry of binary hyperdimensional computing (HDC), a computational scheme in which data are encoded using high-dimensional binary vectors. We establish a result about the similarity structure induced by the HDC binding operator and show that the Laplace kernel naturally arises in this setting, motivating our new encoding method Laplace-HDC, which improves upon previous methods. We describe how our results indicate limitations of binary HDC in encoding spatial information from images and …

abstract arxiv binary computational computing cs.lg data geometry kernel math.pr paper show stat.ml studies type understanding vectors