Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification

• URL: http://arxiv.org/abs/2603.18078v1
• Date: Wed, 18 Mar 2026 07:12:02 GMT
• Title: Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification
• Abstract summary: We present the textbfVariational Phasor Circuit (VPC), a deterministic classical learning architecture operating on the continuous $S1$ unit circle manifold.<n>Inspired by variational quantum circuits, it replaces dense real-valued weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space.<n>We show that benchmarks can decode difficult mental-state classification with competitive accuracy and substantially fewer trainable parameters than standard Euclidean baselines.
• Score: 0.09229852843814058
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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