Efficient Hyperdimensional Computing with Modular Composite Representations

Abstract--The modular composite representation (MCR) is a computing model that represents information with high-dimensional integer vectors using modular arithmetic. Ori gi-nally proposed as a generalization of the binary spatter cod e model, it aims to provide higher representational power whi le remaining a lighter alternative to models requiring high-p recision components. However, despite this potential, MCR has recei ved limited attention in the literature. Systematic analyses o f its trade-offs and comparisons with other models, such as binar y spatter codes, multiply-add-permute, and Fourier hologra phic reduced representation, are lacking, sustaining the perce ption that its added complexity outweighs the improved expressiv ity over simpler models. In this work, we revisit MCR by presenti ng its first extensive evaluation, demonstrating that it achie ves a unique balance of information capacity, classification acc uracy, and hardware efficiency. Experiments measuring informatio n capacity demonstrate that MCR outperforms binary and integ er vectors while approaching complex-valued representation s at a fraction of their memory footprint. Evaluation on a collect ion of 123 classification datasets confirms consistent accuracy gains and shows that MCR can match the performance of binary spatter codes using up to 4.0 less memory. We investigate the hardware realization of MCR by showing that it maps naturally to digital logic and by designing the first dedicat ed accelerator for it. Evaluations on basic operations and sev en selected datasets demonstrate a speedup of up to three order s-of-magnitude and significant energy reductions compared to a software implementation. Furthermore, when matched for accuracy against binary spatter codes, MCR achieves on aver age 3.08 faster execution and 2.68 lower energy consumption. The work of CJK was supported by the Center for the Co-Design o f Cognitive Systems (CoCoSys), one of seven centers in JUMP 2.0, a Se miconductor Research Corporation (SRC) program sponsored by DARP A, in a ddition to the NDSEG Fellowship, Fernström Fellowship, Swartz Founda tion, and NSF Grants 2147640 and 2313149. The work of AL and DK was supporte d by Knut and Alice Wallenberg Foundation under the Wallenber g Scholars program (Grant No. KA W2023.0327).