Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification
This work addresses the problem of efficient signal classification for brain-computer interface applications, offering a mathematically principled alternative to dense neural networks, though it appears incremental as it adapts quantum-inspired concepts to classical settings.
The paper tackled the problem of classifying spatially distributed signals, such as mental states in brain-computer interfaces, by introducing the Variational Phasor Circuit (VPC), a deterministic classical architecture that uses phase shifts and interference on the unit circle. The result showed competitive accuracy with substantially fewer trainable parameters compared to standard Euclidean baselines on synthetic benchmarks.
We present the \textbf{Variational Phasor Circuit (VPC)}, a deterministic classical learning architecture operating on the continuous $S^1$ unit circle manifold. Inspired by variational quantum circuits, VPC replaces dense real-valued weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space. This phase-native design provides a unified method for both binary and multi-class classification of spatially distributed signals. A single VPC block supports compact phase-based decision boundaries, while stacked VPC compositions extend the model to deeper circuits through inter-block pull-back normalization. Using synthetic brain-computer interface benchmarks, we show that VPC can decode difficult mental-state classification tasks with competitive accuracy and substantially fewer trainable parameters than standard Euclidean baselines. These results position unit-circle phase interference as a practical and mathematically principled alternative to dense neural computation, and motivate VPC as both a standalone classifier and a front-end encoding layer for future hybrid phasor-quantum systems.