A wave-geometric duality for hyperdimensional computing
This work provides a physically grounded waveform realization for HDC/VSA operations, addressing the engineering constraints for future hardware implementations.
The paper establishes a unitary embedding from discrete bipolar HDC/VSA vectors to coherent broadband waveforms, realizing core HDC/VSA primitives as wave-domain operations. Full-wave FDTD studies validate the approach, with a coupled Correlation Contrast Ratio of approximately 8.7e-5 for N=1000.
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.