发表机构
Chemnitz University of Technology; Luleå University of Technology; Institute of Information Technologies and Systems; Örebro University; RISE Research Institutes of Sweden; Linköping University（Chemnitz工业大学; 吕勒奥理工大学; 信息技术与系统研究所; 厄勒布鲁大学; 瑞典RISE研究院; 林雪平大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对超维计算中序列表示的时序顺序编码需求，开发三种实值位置编码变体，其中正弦变体可实现高效哈达玛积绑定与精确平移等变，在时间序列分类任务上性能与标准分数幂编码相当。
AI 中文摘要
编码时序顺序是超维计算中序列表示的基本要求。分数幂编码提供了保持相似性的位置向量，其内积近似于平移不变核，且支持编码序列表示的平移等变变换。然而，分数幂编码的标准形式主要针对循环卷积或复值乘法等绑定操作设计，这限制了其与实值向量的哈达玛积绑定的兼容性。本文基于随机傅里叶特征开发了实值位置编码，旨在保留分数幂编码的理想特性，同时支持基于哈达玛的操作。我们提出了三种实值位置编码变体：基于逆傅里叶变换的实值基线，以及从随机傅里叶特征导出的正弦和仅余弦表示。其中，正弦变体提供了显式代数平移算子，允许直接将时序平移应用于向量编码的序列表示，而无需对平移后的序列重新编码。在时间序列分类数据集上的实验表明，所提出的实值表示实现了与标准分数幂编码相当的性能，同时支持计算高效的哈达玛积绑定。正弦变体提供了最有利的权衡，结合了高效的实值实现与精确的平移等变变换。
英文摘要
Encoding temporal order is a fundamental requirement for sequence representations in Hyperdimensional Computing. Fractional Power Encoding provides similarity-preserving position vectors whose inner products approximate shift-invariant kernels, and it supports shift-equivariant transformations of encoded sequence representations. However, standard formulations of Fractional Power Encoding are primarily designed for binding operations such as circular convolution or complex-valued multiplication, which limits their compatibility with Hadamard product binding of real-valued vectors. This paper develops real-valued position encodings motivated by Random Fourier Features, aiming to retain the desirable properties of Fractional Power Encoding while supporting Hadamard-based operations. We propose three real-valued position-encoding variants: a real-valued baseline based on the inverse Fourier transform, and Sinusoid and Cosine-only representations derived from Random Fourier Features. Among them, the Sinusoid variant provides an explicit algebraic shift operator, allowing temporal shifts to be applied directly to the vector-encoded sequence representation without re-encoding the shifted sequence. Experiments on time-series classification datasets show that the proposed real-valued representations achieve performance comparable to standard Fractional Power Encoding while enabling computationally efficient Hadamard product binding. The Sinusoid variant offers the most favorable trade-off, combining efficient real-valued implementation with exact shift-equivariant transformations.
Comments23 pages, 5 figures
