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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.22863 |
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| _version_ | 1866914506103324672 |
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| author | Poore, Tyler L. |
| author_facet | Poore, Tyler L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A wave-geometric duality for hyperdimensional computing Poore, Tyler L. Emerging Technologies Hardware Architecture 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. |
| title | A wave-geometric duality for hyperdimensional computing |
| topic | Emerging Technologies Hardware Architecture |
| url | https://arxiv.org/abs/2604.22863 |