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arXiv · 2604.22863

A wave-geometric duality for hyperdimensional computing

Tyler L. Poore
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Abstract

Hyperdimensional computing (HDC), also referred to as vector symbolic architectures (VSA), represents information with high-dimensional vectors and a compact algebra of primitives. This paper establishes an explicitly unitary embedding from discrete bipolar HDC/VSA vectors to coherent broadband waveforms and develops a common wave-domain realization of the core HDC/VSA primitives within that embedding. Under the resulting RFC/UWE stack, bundling becomes linear superposition, permutation becomes coherent phase evolution, binding is reproduced by nonlinear spectral mixing together with an engineered aliasing step that restores circular-convolution structure, and similarity is recovered as a calibrated differential-power readout. Full-wave FDTD studies validate the physically nontrivial parts of this program, including array-level readout in a mutually coupled setting and the binding pipeline under realistic propagation. In a documented $N=1000$ mutually coupled-array calibration, the predicted interaction effect appears with the expected sign pattern and order of magnitude, yielding a coupled Correlation Contrast Ratio of approximately $8.7 \times 10^{-5}$. The result is a wave-geometric duality for HDC/VSA: existing symbolic operations admit a physically grounded waveform realization, while coherence, isolation, and readout sensitivity remain the central engineering constraints for future hardware.

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Tyler L. Poore. 2026-04-23. A wave-geometric duality for hyperdimensional computing. https://arxiv.org/abs/2604.22863

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