  Hyperdimensional computing (HDC) has emerged as a new light-weight learning
algorithm with smaller computation and energy requirements compared to
conventional techniques. In HDC, data points are represented by
high-dimensional vectors (hypervectors), which are mapped to high-dimensional
space (hyperspace). Typically, a large hypervector dimension ($\geq1000$) is
required to achieve accuracies comparable to conventional alternatives.
However, unnecessarily large hypervectors increase hardware and energy costs,
which can undermine their benefits. This paper presents a technique to minimize
the hypervector dimension while maintaining the accuracy and improving the
robustness of the classifier. To this end, we formulate the hypervector design
as a multi-objective optimization problem for the first time in the literature.
The proposed approach decreases the hypervector dimension by more than
$32\times$ while maintaining or increasing the accuracy achieved by
conventional HDC. Experiments on a commercial hardware platform show that the
proposed approach achieves more than one order of magnitude reduction in model
size, inference time, and energy consumption. We also demonstrate the trade-off
between accuracy and robustness to noise and provide Pareto front solutions as
a design parameter in our hypervector design.
