# Hardware Optimizations of Dense Binary Hyperdimensional Computing: Rematerialization of Hypervectors, Binarized Bundling, and Combinational Associative Memory

arXiv: https://arxiv.org/abs/1807.08583 · HTML: https://mlsanity.com/paper/1807.08583/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2018.

## Built on by (most cited first, 14 of 14)

- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [Vector Symbolic Architectures as a Computing Framework for Emerging Hardware](https://mlsanity.com/paper/2106.05268/) (2021)
- [GraphHD: Efficient graph classification using hyperdimensional computing](https://mlsanity.com/paper/2205.07826/) (2022)
- [Generalized Learning Vector Quantization for Classification in Randomized Neural Networks and Hyperdimensional Computing](https://mlsanity.com/paper/2106.09821/) (2021)
- [Learning from Hypervectors: A Survey on Hypervector Encoding](https://mlsanity.com/paper/2308.00685/) (2023)
- [A 5 μ W Standard Cell Memory-based Configurable Hyperdimensional Computing Accelerator for Always-on Smart Sensing](https://mlsanity.com/paper/2102.02758/) (2021)
- [Streaming Encoding Algorithms for Scalable Hyperdimensional Computing](https://mlsanity.com/paper/2209.09868/) (2022)
- [Sobol Sequence Optimization for Hardware-Efficient Vector Symbolic Architectures](https://mlsanity.com/paper/2311.10277/) (2023)
- [Efficient Hyperdimensional Computing](https://mlsanity.com/paper/2301.10902/) (2023)
- [AMS-HD: Hyperdimensional Computing for Real-Time and Energy-Efficient Acute Mountain Sickness Detection](https://mlsanity.com/paper/2602.08916/) (2026)
- [HDXplore: Automated Blackbox Testing of Brain-Inspired Hyperdimensional Computing](https://mlsanity.com/paper/2105.12770/) (2021)
- [Brain-Inspired Hyperdimensional Computing: How Thermal-Friendly for Edge Computing?](https://mlsanity.com/paper/2204.03739/) (2022)
- [Robust Clustering using Hyperdimensional Computing](https://mlsanity.com/paper/2312.02407/) (2023)
- [Zero-shot Classification using Hyperdimensional Computing](https://mlsanity.com/paper/2401.16876/) (2024)

## Abstract (arXiv)

Brain-inspired hyperdimensional (HD) computing models neural activity patterns of the very size of the brain's circuits with points of a hyperdimensional space, that is, with hypervectors. Hypervectors are D-dimensional (pseudo)random vectors with independent and identically distributed (i.i.d.) components constituting ultra-wide holographic words: D = 10,000 bits, for instance. At its very core, HD computing manipulates a set of seed hypervectors to build composite hypervectors representing objects of interest. It demands memory optimizations with simple operations for an e cient hardware realization. In this paper, we propose hardware techniques for optimizations of HD computing, in a synthesizable VHDL library, to enable co-located implementation of both learning and classification tasks on only a small portion of Xilinx(R) UltraScale(TM) FPGAs: (1) We propose simple logical operations to rematerialize the hypervectors on the fly rather than loading them from memory. These operations massively reduce the memory footprint by directly computing the composite hypervectors whose individual seed hypervectors do not need to be stored in memory. (2) Bundling a series of hypervectors over time requires a multibit counter per every hypervector component. We instead propose a binarized back-to-back bundling without requiring any counters. This truly enables on-chip learning with minimal resources as every hypervector component remains binary over the course of training to avoid otherwise multibit component. (3) For every classification event, an associative memory is in charge of finding the closest match between a set of learned hypervectors and a query hypervector by using a distance metric. This operator is proportional to [...]