Computing with Residue Numbers in High-Dimensional Representation
This work addresses computational challenges in visual perception and combinatorial optimization, offering a potential account for brain grid cells and new machine learning architectures, though it appears incremental in its application of existing concepts.
The paper tackles the problem of representing and operating on numerical values with high dynamic range by introducing Residue Hyperdimensional Computing, which unifies residue number systems with high-dimensional vector algebra, resulting in fewer resources and robustness to noise compared to previous methods.
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.