Hardware-Aware Static Optimization of Hyperdimensional Computations

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.