Hyperdimensional computing (HDC) uses binary vectors of high dimensions to perform classification. Due to its simplicity and massive parallelism, HDC can be highly energy-efficient and well-suited for resource-constrained platforms. However, in trading off orthogonality with efficiency, hypervectors may use tens of thousands of dimensions. In this paper, we will examine the necessity for such high dimensions. In particular, we give a detailed theoretical analysis of the relationship among dimensions of hypervectors, accuracy, and orthogonality. The main conclusion of this study is that a much lower dimension, typically less than 100, can also achieve similar or even higher detecting accuracy compared with other state-of-the-art HDC models. Based on this insight, we propose a suite of novel techniques to build HDC models that use binary hypervectors of dimensions that are orders of magnitude smaller than those found in the state-of-the-art HDC models, yet yield equivalent or even improved accuracy and efficiency. For image classification, we achieved an HDC accuracy of 96.88\% with a dimension of only 32 on the MNIST dataset. We further explore our methods on more complex datasets like CIFAR-10 and show the limits of HDC computing.

翻译：超维计算（HDC）使用高维二进制向量进行分类。由于其简单性和大规模并行性，HDC可具备高能效，特别适合资源受限平台。然而，为权衡正交性与效率，超向量可能使用数万维数。本文旨在探讨此类高维度的必要性。具体而言，我们详细理论分析了超向量维度、准确率与正交性之间的关系。研究主要结论表明：相较于其他最先进HDC模型，低得多（通常低于100维）的维度也能实现相似甚至更高的检测精度。基于此发现，我们提出一套新技术，构建采用二进制超向量的HDC模型，其维度比现有最优HDC模型低数个数量级，却能达到等同或更优的准确率与效率。在图像分类任务中，我们针对MNIST数据集，使用仅32维的HDC实现了96.88%的准确率。我们进一步在CIFAR-10等更复杂数据集上探索该方法，并揭示HDC计算的局限性。