Hyperdimensional computing (HDC) is a method to perform classification that uses binary vectors with high dimensions and the majority rule. This approach has the potential to be energy-efficient and hence deemed suitable for resource-limited platforms due to its simplicity and massive parallelism. However, in order to achieve high accuracy, HDC sometimes uses hypervectors with tens of thousands of dimensions. This potentially negates its efficiency advantage. In this paper, we examine the necessity of such high dimensions and conduct a detailed theoretical analysis of the relationship between hypervector dimensions and accuracy. Our results demonstrate that as the dimension of the hypervectors increases, the worst-case/average-case HDC prediction accuracy with the majority rule decreases. Building on this insight, we develop HDC models that use binary hypervectors with dimensions orders of magnitude lower than those of state-of-the-art HDC models while maintaining equivalent or even improved accuracy and efficiency. For instance, on the MNIST dataset, we achieve 91.12% HDC accuracy in image classification with a dimension of only 64. Our methods perform operations that are only 0.35% of other HDC models with dimensions of 10,000. Furthermore, we evaluate our methods on ISOLET, UCI-HAR, and Fashion-MNIST datasets and investigate the limits of HDC computing.

翻译：超维计算（HDC）是一种利用高维二元向量和多数投票规则进行分类的方法。该方法因其简洁性和大规模并行性而具有能效潜力，因此被认为适用于资源受限平台。然而，为实现高精度，HDC有时需使用数万维的超向量，这可能会抵消其效率优势。本文研究了高维度的必要性，并对超向量维度与精度之间的关系进行了详细的理论分析。结果表明，随着超向量维度增加，基于多数投票规则的HDC预测精度在最坏/平均情况下均会下降。基于这一发现，我们开发了使用维度比当前最先进HDC模型低数个数量级的二元超向量的HDC模型，同时保持等同甚至更优的精度和效率。例如，在MNIST数据集上，我们仅用64维便实现了91.12%的图像分类HDC精度。我们的方法执行的操作量仅为维度为10,000的其他HDC模型的0.35%。此外，我们还在ISOLET、UCI-HAR和Fashion-MNIST数据集上评估了方法，并探究了HDC计算的极限。