Real-Valued Hyperdimensional Sequence Representations with Hadamard Product Binding and Shift Equivariance

2026-08-28

AI Summary

本文解决了Hyperdimensional Computing中实值向量绑定操作兼容性问题，通过引入基于随机傅里叶特征的实值位置编码方法，并验证了其在时间序列分类任务中的有效性。

Abstract

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.

Problem

• Hyperdimensional Computing
• Fractional Power Encoding
• Hadamard product binding
• shift-equivariance
• Random Fourier Features

Innovation

• Real-Valued Position Encodings
• Hadamard Product Binding
• Shift Equivariance
• Sinusoid Variant
• Random Fourier Features