Sobol Sequence Optimization for Hardware-Efficient Vector Symbolic
  Architectures
Sercan Aygun M. Hassan Najafi
Hyperdimensional computing (HDC) is an emerging computing paradigm with
significant promise for efficient and robust learning. In HDC, objects are
encoded with high-dimensional vector symbolic sequences called hypervectors.
The quality of hypervectors, defined by their distribution and independence,
directly impacts the performance of HDC systems. Despite a large body of work
on the processing parts of HDC systems, little to no attention has been paid to
data encoding and the quality of hypervectors. Most prior studies have
generated hypervectors using inherent random functions, such as MATLAB`s or
Python`s random function. This work introduces an optimization technique for
generating hypervectors by employing quasi-random sequences. These sequences
have recently demonstrated their effectiveness in achieving accurate and
low-discrepancy data encoding in stochastic computing systems. The study
outlines the optimization steps for utilizing Sobol sequences to produce
high-quality hypervectors in HDC systems. An optimization algorithm is proposed
to select the most suitable Sobol sequences for generating minimally correlated
hypervectors, particularly in applications related to symbol-oriented
architectures. The performance of the proposed technique is evaluated in
comparison to two traditional approaches of generating hypervectors based on
linear-feedback shift registers and MATLAB random function. The evaluation is
conducted for two applications: (i) language and (ii) headline classification.
Our experimental results demonstrate accuracy improvements of up to 10.79%,
depending on the vector size. Additionally, the proposed encoding hardware
exhibits reduced energy consumption and a superior area-delay product.