Laplace-HDC: Understanding the geometry of binary hyperdimensional computing

TL;DR

This paper explores the geometry of binary hyperdimensional computing, introduces Laplace-HDC which enhances encoding accuracy, and discusses limitations and solutions for spatial information encoding in high-dimensional binary vectors.

Contribution

The paper introduces Laplace-HDC, a novel encoding method that leverages the Laplace kernel, improving accuracy and robustness in binary hyperdimensional computing.

Findings

Laplace-HDC outperforms previous encoding methods in accuracy.

The Laplace kernel naturally arises in the similarity structure of binary HDC.

Limitations in encoding spatial information are identified and potential solutions are discussed.

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 discuss potential solutions, including using Haar convolutional features and the definition of a translation-equivariant HDC encoding. Several numerical experiments highlighting the improved accuracy of Laplace-HDC in contrast to alternative methods are presented. We also numerically study other aspects of the proposed framework such as robustness and the underlying translation-equivariant encoding.