This paper presents a quantum algorithm for efficiently decoding
hypervectors, a crucial process in extracting atomic elements from hypervectors
- an essential task in Hyperdimensional Computing (HDC) models for
interpretable learning and information retrieval. HDC employs high-dimensional
vectors and efficient operators to encode and manipulate information,
representing complex objects from atomic concepts. When one attempts to decode
a hypervector that is the product (binding) of multiple hypervectors, the
factorization becomes prohibitively costly with classical optimization-based
methods and specialized recurrent networks, an inherent consequence of the
binding operation. We propose HDQF, an innovative quantum computing approach,
to address this challenge. By exploiting parallels between HDC and quantum
computing and capitalizing on quantum algorithms' speedup capabilities, HDQF
encodes potential factors as a quantum superposition using qubit states and
bipolar vector representation. This yields a quadratic speedup over classical
search methods and effectively mitigates Hypervector Factorization capacity
issues.

本文提出了一种量子算法，用于有效地解码超向量，这是从超向量中提取原子元素的关键过程，是可解释学习和信息检索中超维计算（HDC）模型的重要任务。我们通过利用 HDC 和量子计算之间的相似之处，并利用量子算法的加速能力，提出了 HDQF，一种创新的量子计算方法，以解决超维素分解容量问题，实现了二次加速。

超维量子因式分解

Hyperdimensional Quantum Factorization

Hyperdimensional computing (HDC) is an emerging computing paradigm with
significant promise for efficient and robust learning. In HDC, objects are
encoded with high-dimensional vector symbolic sequences called hypervectors.
The quality of hypervectors, defined by their distribution and independence,
directly impacts the performance of HDC systems. Despite a large body of work
on the processing parts of HDC systems, little to no attention has been paid to
data encoding and the quality of hypervectors. Most prior studies have
generated hypervectors using inherent random functions, such as MATLAB`s or
Python`s random function. This work introduces an optimization technique for
generating hypervectors by employing quasi-random sequences. These sequences
have recently demonstrated their effectiveness in achieving accurate and
low-discrepancy data encoding in stochastic computing systems. The study
outlines the optimization steps for utilizing Sobol sequences to produce
high-quality hypervectors in HDC systems. An optimization algorithm is proposed
to select the most suitable Sobol sequences for generating minimally correlated
hypervectors, particularly in applications related to symbol-oriented
architectures. The performance of the proposed technique is evaluated in
comparison to two traditional approaches of generating hypervectors based on
linear-feedback shift registers and MATLAB random function. The evaluation is
conducted for two applications: (i) language and (ii) headline classification.
Our experimental results demonstrate accuracy improvements of up to 10.79%,
depending on the vector size. Additionally, the proposed encoding hardware
exhibits reduced energy consumption and a superior area-delay product.

使用优化算法和 Sobol 序列生成高质量超向量，改进了超维计算中的数据编码和性能，提高语言和标题分类的准确性并降低能量消耗。

硬件高效向量符号架构的 Sobol 序列优化

Sobol Sequence Optimization for Hardware-Efficient Vector Symbolic  Architectures

Hyperdimensional computing (HDC) is a novel computational paradigm that
operates on long-dimensional vectors known as hypervectors. The hypervectors
are constructed as long bit-streams and form the basic building blocks of HDC
systems. In HDC, hypervectors are generated from scalar values without taking
their bit significance into consideration. HDC has been shown to be efficient
and robust in various data processing applications, including computer vision
tasks. To construct HDC models for vision applications, the current
state-of-the-art practice utilizes two parameters for data encoding: pixel
intensity and pixel position. However, the intensity and position information
embedded in high-dimensional vectors are generally not generated dynamically in
the HDC models. Consequently, the optimal design of hypervectors with high
model accuracy requires powerful computing platforms for training. A more
efficient approach to generating hypervectors is to create them dynamically
during the training phase, which results in accurate, low-cost, and highly
performable vectors. To this aim, we use low-discrepancy sequences to generate
intensity hypervectors only, while avoiding position hypervectors. By doing so,
the multiplication step in vector encoding is eliminated, resulting in a
power-efficient HDC system. For the first time in the literature, our proposed
approach employs lightweight vector generators utilizing unary bit-streams for
efficient encoding of data instead of using conventional comparator-based
generators.

高维计算是一种新的计算范式，通过长向量（称为超向量）进行操作。该论文提出了一种基于轻量级向量生成器的高效编码方法，以减少计算平台的要求，并改进超向量的性能。

uHD: 轻量级和动态超高维度计算的一元处理

uHD: Unary Processing for Lightweight and Dynamic Hyperdimensional  Computing

Hyperdimensional computing (HDC) is an emerging computing paradigm that
imitates the brain's structure to offer a powerful and efficient processing and
learning model. In HDC, the data are encoded with long vectors, called
hypervectors, typically with a length of 1K to 10K. The literature provides
several encoding techniques to generate orthogonal or correlated hypervectors,
depending on the intended application. The existing surveys in the literature
often focus on the overall aspects of HDC systems, including system inputs,
primary computations, and final outputs. However, this study takes a more
specific approach. It zeroes in on the HDC system input and the generation of
hypervectors, directly influencing the hypervector encoding process. This
survey brings together various methods for hypervector generation from
different studies and explores the limitations, challenges, and potential
benefits they entail. Through a comprehensive exploration of this survey,
readers will acquire a profound understanding of various encoding types in HDC
and gain insights into the intricate process of hypervector generation for
diverse applications.

超维度计算（HDC）是一种模拟大脑结构，提供强大高效的处理和学习模型的新兴计算范式。本文聚焦于 HDC 系统输入和超向量生成两个方面，探讨各种生成超向量的方法，并探索其局限性、挑战和潜在优势，以深入理解 HDC 中各种编码类型及多样的应用领域中复杂的超向量生成过程。