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

2026-03-18

AI Summary

This work addresses the trade-off between parameter efficiency and model expressivity in phase-based neural signal classification for brain–computer interfaces by proposing a phase-native classical learning architecture operating on the unit circle (S¹) manifold. The approach uniquely translates concepts from variational quantum circuits into a classical phase circuit, constructing compact decision boundaries through trainable phase shifts, local unitary mixing, and structured interference, while supporting deep stacking. Inter-block Laplacian normalization is introduced to stabilize training dynamics. Evaluated on synthetic brain–computer interface benchmark tasks, the model achieves classification accuracy comparable to Euclidean-space baselines while substantially reducing the number of trainable parameters, thereby enabling efficient yet expressive modeling of phase-encoded neural signals.

Technology Category

Machine Learning: Learning with ManifoldsCognitive Modeling & Cognitive Systems: Neural Spike CodingNatural Language Processing: Learning & Optimization for NLP

Application Category

User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsEconomics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• brain-computer interface
• phase-based classification
• mental-state decoding
• parameter-efficient learning
• spatially distributed signals

Innovation

• Variational Phasor Circuit
• phase-native computation
• unit-circle manifold
• structured interference
• brain-computer interface