# Laplace-HDC: Understanding the geometry of binary hyperdimensional computing

arXiv: https://arxiv.org/abs/2404.10759 · HTML: https://mlsanity.com/paper/2404.10759/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [On the Similarity between the Laplace and Neural Tangent Kernels](https://mlsanity.com/paper/2007.01580/) (2020)
- [Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS](https://mlsanity.com/paper/2009.10683/) (2020)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [Classification using Hyperdimensional Computing: A Review](https://mlsanity.com/paper/2004.11204/) (2020)
- [A Theoretical Perspective on Hyperdimensional Computing](https://mlsanity.com/paper/2010.07426/) (2020)
- [SpinalNet: Deep Neural Network with Gradual Input](https://mlsanity.com/paper/2007.03347/) (2020)
- [Hyperdimensional computing as a framework for systematic aggregation of image descriptors](https://mlsanity.com/paper/2101.07720/) (2021)
- [Bitwise Neural Networks](https://mlsanity.com/paper/1601.06071/) (2016)
- [No Routing Needed Between Capsules](https://mlsanity.com/paper/2001.09136/) (2020)
- [Understanding Hyperdimensional Computing for Parallel Single-Pass Learning](https://mlsanity.com/paper/2202.04805/) (2022)
- [Hypervector Design for Efficient Hyperdimensional Computing on Edge Devices](https://mlsanity.com/paper/2103.06709/) (2021)
- [Holographic Graph Neuron: a Bio-Inspired Architecture for Pattern Processing](https://mlsanity.com/paper/1501.03784/) (2015)
- [Ensemble learning in CNN augmented with fully connected subnetworks](https://mlsanity.com/paper/2003.08562/) (2020)

## Built on by (most cited first, 4 of 4)

- [On Design Choices in Similarity-Preserving Sparse Randomized Embeddings](https://mlsanity.com/paper/2501.14741/) (2024)
- [Large-Margin Hyperdimensional Computing: A Learning-Theoretical Perspective](https://mlsanity.com/paper/2603.03830/) (2026)
- [ImageHD: Energy-Efficient On-Device Continual Learning of Visual Representations via Hyperdimensional Computing](https://mlsanity.com/paper/2604.21280/) (2026)
- [Primitive-Driven Acceleration of Hyperdimensional Computing for Real-Time Image Classification](https://mlsanity.com/paper/2601.20061/) (2026)

## Abstract (arXiv)

This paper studies the geometry of binary hyperdimensional computing (HDC), a computational scheme in which data are encoded using high-dimensional binary vectors. We establish a result about the similarity structure induced by the HDC binding operator and show that the Laplace kernel naturally arises in this setting, motivating our new encoding method Laplace-HDC, which improves upon previous methods. We describe how our results indicate limitations of binary HDC in encoding spatial information from images and discuss potential solutions, including using Haar convolutional features and the definition of a translation-equivariant HDC encoding. Several numerical experiments highlighting the improved accuracy of Laplace-HDC in contrast to alternative methods are presented. We also numerically study other aspects of the proposed framework such as robustness and the underlying translation-equivariant encoding.