Computing with Residue Numbers in High-Dimensional Representation
Christopher J. Kymn Denis Kleyko E. Paxon Frady Connor Bybee Pentti Kanerva Friedrich T. Sommer Bruno A. Olshausen
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.