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

arXiv · AI, language, vision and robotics · article · Aug 28, 2026 · UTC

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 d

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