Hyperdimensional (HD) computing is an highly error-resilient computational paradigm that can be used to efficiently perform language classification, data retrieval, and analogical reasoning tasks on error-prone emerging hardware technologies. HD computation is storage-inefficient and often requires computing over 10,000-dimensional bit vectors. Prior work either leaves hypervectors unoptimized or dynamically tunes HD computation parameters (e.g., hypervector dimension) to deliver the desired accuracy. These approaches are time-consuming, lack accuracy guarantees, and do not generalize well. We present Heim, a framework for statically optimizing HD computation parameters to minimize resource usage in the presence of hardware error. Heim guarantees the optimized computation satisfies a user-provided target accuracy. Heim deploys a novel analysis procedure that unifies theoretical results in HD computing to systematically optimize HD computation. We develop four analysis-amenable data structures that leverage Heim to perform aggressive space-saving optimizations, and optimize these data structures to attain 99% query accuracy on both binary memory and multiple-bit-per-cell resistive memory. Heim-optimized data structures deliver 1.31x-14.51x reductions in hypervector size and 2.191x-27.27x reductions in memory usage while attaining 98.96-99.75% accuracy. Heim-optimized data structures deliver up to 41.40% accuracy improvements over dynamically tuned parameters. Heim computes parameters significantly faster than dynamic approaches.

翻译：超维（HD）计算是一种高度容错的计算范式，能够高效地在易出错的非传统硬件技术上执行语言分类、数据检索和类比推理任务。HD计算存在存储效率低的问题，通常需要处理超过一万维的比特向量。现有研究要么对超向量不加优化，要么动态调整HD计算参数（如超向量维度）以达到期望精度。这些方法耗时、缺乏精度保证且泛化能力弱。我们提出Heim框架，用于在硬件错误存在时静态优化HD计算参数，以最小化资源使用。Heim保证优化后的计算满足用户提供的目标精度。Heim采用一种新颖的分析流程，融合HD计算的理论成果以系统优化HD计算。我们开发了四种易于分析的数据结构，利用Heim进行激进的节省空间优化，并优化这些数据结构，使其在二进制存储器和多位每单元电阻式存储器上均达到99%的查询精度。经Heim优化的数据结构将超向量大小降低1.31倍至14.51倍，内存使用降低2.191倍至27.27倍，同时保持98.96%至99.75%的精度。与动态调优参数相比，Heim优化的数据结构精度提升高达41.40%。此外，Heim计算参数的速度显著快于动态方法。