Sobol Sequence Optimization for Hardware-Efficient Vector Symbolic Architectures

Abstract: 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 MATLABs or Pythons 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.