Computing with Residue Numbers in High-Dimensional Representation

TL;DR

This paper presents Residue Hyperdimensional Computing, a novel framework that combines residue number systems with high-dimensional vectors, enabling efficient, robust, and scalable numerical computations with applications in perception, optimization, and neuroscience.

Contribution

It introduces a new algebraic framework unifying residue number systems with high-dimensional vectors, enabling resource-efficient and noise-robust numerical operations.

Findings

Efficient representation of large dynamic range numbers with fewer resources.

Robustness to noise in high-dimensional vector operations.

Improved performance in visual perception and combinatorial optimization tasks.

Abstract

We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using vastly fewer resources than previous methods, and it exhibits impressive robustness to noise. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.