A wave-geometric duality for hyperdimensional computing

TL;DR

This paper introduces a wave-geometric duality for hyperdimensional computing, translating vector operations into physical waveforms and validating the approach with FDTD simulations.

Contribution

It develops a unitary embedding of HDC/VSA vectors into waveforms and realizes core primitives through physical wave interactions, bridging symbolic and physical representations.

Findings

Validated array-level readout in coupled arrays

Demonstrated nonlinear spectral mixing for binding

Achieved a correlation contrast ratio of approximately 8.7e-5

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.